2. STRUCTURE OF ATOM

(A) SUBATOMIC PARTICLES1. Why does the atomic charge-to-mass ratio of positive rays depend on the residual gas in the

discharge tube? Why is the charge-to-mass ratio of all cathode rays the same?2. In one discharge tube, H2 gas is taken and in the other O2 gas is taken. Will the electrons and

positive ions in the cathode rays and in the anode rays be the same or different?3. (a) Calculate the number of electrons which will together weigh one gram.

(b) Calculate the mass and charge of one mole of electrons .(NCERT)

4. (a) Calculate the total number of electrons present in 1 mol of methane.(b) Find (i) the total number and (ii) the total mass of neutrons in 7 mg of 14C. (Assume that mass of

a neutron = 1.675 × 10–27 kg.)(c) Find (i) the total number and (ii) the total mass of protons in 34 mg of NH3 at STP.Will the answer change if the temperature and pressure are changed?

(NCERT)5. If the diameter of a carbon atom is 0.15 nm, calculate the number of carbon atoms which can be

placed side by side in a straight line across scale of length 20 cm long.(NCERT)

6. If 2 × 108 atoms of carbon are arranged side by side, calculate the radius of carbon atom when the length of this arrangement is 2.4 cm.

(NCERT)7. The diameter of zinc atom is 2.6 Å. Calculate (a) radius of zinc atom in pm and (b) number of atoms

present in a length of 1.6 cm if the zinc atoms are arranged side by side lengthwise.(NCERT)

8. A certain particle carries 2.5 × 10–16 C of static electric charge. Calculate the number of electrons present in it.

(NCERT)9. In Millikan’s experiment, static electric charge on the oil drops has been obtained by shining X-

rays. If the static electric charge on the oil drop is –1.282 × 10–18 C, calculate the number of electrons present on it.

(NCERT)10. Explain the experiment that leads to the discovery of electrons.11. What were the characteristics observed in the modified cathode ray experiment that leads to the

discovery of protons?12. Calculate the number of electrons in a charged particle having a static electric charge of 7.25 × 10 -16

C.13. Compute the charge on one mole of electrons, if the charge on an electron is 1.602 × 10-19 C.14. Compare and contrast the mass, electrical charge and location of the three major subatomic

particles.15. What is the evidence that cathode rays are a part of matter?16. Why cathode rays are produced only when the pressure of the gas inside the discharge tube is very

low?17. What is the difference in the origin of cathode rays and anode rays?

18. Give two examples from everyday life where cathode rays are used?19. What is the actual value of charge and mass of an electron?20. Name the experiment that led to the discovery of neutrons.21. What did Thomson’s experiment on the deflection of cathode rays yield?22. Explain the origin of cathode rays.23. Compare the properties of electrons, protons and neutrons.24. Briefly describe the experiment that led to discovery of a proton.25. Compare the properties of cathode and anode rays.26. Describe Millikan experiment to determine the charge on an electron.27. Describe how protons and neutrons were discovered to be constituents of an atom.28. Explain the functioning of a cathode ray tube and the experiment that led to the discovery of an

electron.29. What are anode rays? How do they originate? List their important properties.

(B) ATOMIC MODELS30. When α-rays hit a thin foil of gold, very few α-particles are deflected back. What does it prove?31. Neutrons can be found in all atomic nuclei except in one case. Which is this atomic nucleus and

what does it consist of?32. A monoatomic anion of unit charge contains 45 neutrons and 36 electrons. Find the atomic number,

mass number of the anion with its identification.33. How many neutrons and protons are there in the following nuclei?

613 C, 8

16 O, 1224 Mg, 26

56 Fe, 3888 Sr

(NCERT)34. Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A): (a)

Z = 17, A = 35; (b) Z = 92, A = 233; (c) Z = 4, A = 9.(NCERT)

35. In Rutherford’s experiment, generally the thin foil of heavy atoms, like gold, platinum etc. have been used to be bombarded by the α-particles. If the thin foil of light atoms like aluminium etc. is used, what difference would be observed from the above results?

(NCERT)

36. Symbols 3579 Br

and 79 Br can be written, whereas symbols 79

35 Brand 35 Br

are not acceptable. Answer briefly.

(NCERT)37. An element with mass number 81 contains 31.7% more neutrons as compared to protons. Assign

the atomic symbol. (NCERT)

38. An ion with mass number 37 possesses one unit of negative charge. If the ion contains 11.1% more neutrons than the electrons, find the symbol of the ion.

(NCERT)39. An ion with mass number 56 contains 3 units of positive charge and 30.4% more neutrons than

electrons. Assign the symbol to this ion.(NCERT)

40. Explain in detail the findings of Thomson’s model of the atom. What was its shortcoming?

41. According to Rutherford’s model of the atom, where is the positive charge concentrated? What does it predict about the relative size of the nucleus and the radius of the atom? What is the nucleus composed of according to this model?

42. Where in an atom is nearly all of its mass concentrated? Explain your answer in terms of the particles that contribute to this mass.

43. Consider the symbolba X

, where X stands for the chemical symbol for an element. What information is given in locations a and b?

44. Calculate the percentage of higher isotope of neon which has atomic mass 20.2 and the isotopes have the mass numbers 20 and 22.

45. Compute the number of protons and neutrons in the following:1327 Al, 11

23 Na, 2656 Fe, 17

35 Cl.

46. Explain why the atomic masses of elements are not whole numbers.47. How are the different isotopes of an element alike; how are they different?48. Explain how Rutherford’s gold foil experiment changed the model of the atom proposed by

Thomson.49. What are the different isotopes of hydrogen?50. What is the number of neutrons are present in 92U238?51. Nuclear radius is of the order of 10-13 cm while atomic radius is of the order of 10-8 cm. Assuming

the nucleus and the atom to be spherical, what fraction of the atomic volume is occupied by the nucleus?

52. How many nucleons are present in an atom of Nobelium, 102254

No?53. What is Thomson’s model of atom?54. Describe the experimental basis for the fact that nucleus is heavy but occupies a very small fraction

of the volume of the atom.55. What are isotopes? How are they represented?56. What were the shortcomings of Rutherford’s model of atom?57. Describe Rutherford’s scattering experiment and its important observations and influences.

(C) DEVELOPMENTS LEADING TO BOHR’S MODEL OF ATOM58. What is the main difference between electromagnetic wave theory and Planck’s quantum theory?59. Arrange X-rays and radiowaves in order of decreasing frequency.60. Calculate the wavelength from the Balmer formula when n = 3.61. Calculate the wave number of radiations having a frequency of 4 × 1014 Hz.62. Light of wavelength 4000 Ǻ falls on the surface of caesium. Calculate the energy of the

photoelectron emitted. The critical wavelength for photoelectric effect in caesium is 6600 Ǻ.63. Chlorophyll present in green leaves of plants absorbs light at 4.620 × 1014 Hz. Calculate the

wavelength of radiation in nanometer. Which part of the electromagnetic spectrum does it belong to?

64. Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency

(ν) and wavenumber ( v̄ ) of the yellow light.(NCERT)

65. Find energy of each of the photons which (a) correspond to light of frequency 3 × 1015 Hz and (b) have wavelength of 0.50 Å.

(NCERT)66. Calculate the wavelength, frequency and wavenumber of a light wave whose period is 2.0 × 10–10

s.

(NCERT)67. What is the number of photons of light with a wavelength of 4000 pm that provide 1 J of energy?

(NCERT)68. A photon of wavelength 4 × 10–7 m strikes on metal surface, the work function of the metal being

2.13 eV. Calculate (a) the energy of the photon (eV), (b) the kinetic energy of the emission, and (c) the velocity of the photoelectron (1 eV= 1.6020 × 10–19 J).

(NCERT)69. Electromagnetic radiation of wavelength 242 nm is just sufficient to ionize the sodium atom.

Calculate the ionization energy of sodium in kJ mol–1.(NCERT)

70. A 25 W bulb emits monochromatic yellow light of wavelength of 0.57μm. Calculate the rate of emission of quanta per second.

(NCERT)71. Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of

wavelength 6800 Å. Calculate threshold frequency (ν0) and work function (W0) of the metal.

(NCERT)72. What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition

from an energy level with n = 4 to an energy level with n = 2?(NCERT)

73. Arrange the following type of radiations in increasing order of frequency: (a) radiation from microwave oven, (b) amber light from traffic signal, (c) radiation from FM radio, (d) cosmic rays from outer space and (e) X-rays.

(NCERT)74. Nitrogen laser produces a radiation at a wavelength of 337.1 nm. If the number of photons emitted

is 5.6 × 1024, calculate the power of this laser.(NCERT)

75. Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate (a) the frequency of emission, (b) distance traveled by this radiation in 30 s, (c) energy of quantum and (d) number of quanta present if it produces 2 J of energy.

(NCERT)76. In astronomical observations, signals observed from the distant stars are generally weak. If the

photon detector receives a total of 3.15 × 10–18 J from the radiations of 600 nm, calculate the number of photons received by the detector.

(NCERT)

77. Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nano second range. If the radiation source has the duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 1015, calculate the energy of the source.

(NCERT)78. The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate

the frequency of each transition and energy difference between two excited states.(NCERT)

79. The work function for caesium atom is 1.9 eV. Calculate (a) the threshold wavelength and (b) the threshold frequency of the radiation. If the caesium element is irradiated with a wavelength 500 nm, calculate the kinetic energy and the velocity of the ejected photoelectron.

(NCERT)80. Following results are observed when sodium metal is irradiated with different wavelengths.

Calculate (a) threshold wavelength and, (b) Planck’s constant.

(NCERT)81. The ejection of the photoelectron from the

silver metal in the photoelectric effect experiment can be stopped by applying the voltage of 0.35 V when the radiation 256.7 nm is used. Calculate the work function for silver metal.

(NCERT)82. If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is

ejected out with a velocity of 1.5 × 107 m s–1, calculate the energy with which it is bound to the nucleus.

(NCERT)83. Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be

represented as

v = 3.29 × 1015 Hz ( 1

32 -

1

n2 )Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.

(NCERT)84. (a) Calculate the frequency of light whose wavelength is 456 cm.

(b) Calculate the wavelength of a radio wave with frequency 13.68 kHz.85. In the visible spectrum, the wavelength of violet light is 450 nm and that of red light is 750 nm.

Calculate the frequency and wave number of these radiations.86. What is an atomic spectrum? How does it differ from a continuous spectrum? What fundamental

fact is implied by the existence of atomic spectra?87. (a) Name the first five series of lines that occur in the atomic spectrum of hydrogen and indicate the

region in the electromagnetic spectrum where these series occur.(b) Give the general equation for the wave number applicable to all the series.

λ (nm) 500 450 400v 10–5 (cm s–1) 2.55 4.35 5.35

88. The meter has been defined as 1650763.73 wavelengths of the orange – red line of the emission spectrum of 86Kr. Calculate the frequency of this radiation. In what portion of the electromagnetic spectrum does the radiation fall?

89. What are the assumptions on which the Bohr theory of the structure of the hydrogen atom is based?90. Give the equation which explains the different series of lines in the atomic spectrum of hydrogen.

Who is the equation named after? Explain the various terms involved.91. The Balmer series of spectral lines for hydrogen appear in the visible region. What is the lower

energy level that this electronic transition starts from, and what transitions correspond to the spectral lines at 379.0 nm and 430.0 nm, respectively?

92. What is the wave number and wavelength of the first transition in the Lyman, Balmer, and Paschen series in the atomic spectra of hydrogen?

93. Calculate the longest wavelength of light emitted by a hydrogen atom when it undergoes a transition from n = 7 level.

94. What is photoelectric effect? Calculate the frequency and energy of a photon of light with wavelength 520 nm.

95. The minimum energy required to eject an electron from a metal is 4.34 × 10 -19J. What is the minimum frequency of light required for photoelectric effect in the metal?

96. Calculate the value of Planck’s constant if the wavelength of light is 1 × 10-10m and the momentum is 6.6 × 10-24kg m s-1.

97. If the binding energy of electrons in a metal is 250kJ mol -1, what should be threshold frequency of the striking photons?

98. What do you understand by blackbody and blackbody radiations?99. Write a short note on atomic spectrum.100. Name the two experimental phenomena which can be explained by the wave nature of the

electromagnetic radiation. 101. What is the value of Planck’s constant in SI units?102. What is the Rydbergs formula?103. What was the main achievement of the Planck’s quantum theory?104. Which has the greater energy - a photon of violet light or a photon of green light?105. What is the difference between the emission spectrum and absorption spectrum?106. How does the intensity of the spectral line vary with wavelength?107. Briefly explain the Planck’s quantum theory. What is meant by quantum? What are units of

Planck’s constant?108. How is the atomic spectrum of hydrogen obtained? What are the different series of lines present in it

and the regions in which they lie?109. What is the difference between Rydberg formula and Balmer formula?110. A photon of wavelength 1.4Ǻ collides with a stationary electron. After collision, the wavelength of

the photon is found to be 2.0Ǻ. Calculate the energy of the scattered electron.111. Sodium Street lamp gives off a characteristic yellow light of wavelength 588 nm. Calculate the

energy per mole (in kJ mol-1) of these photons.112. When a certain metal was irradiated with a light of frequency 3.2 × 10 16 Hz, the photoelectrons had

twice the kinetic energy as emitted when the same metal was irradiated with light of frequency 2.0

× 1016 Hz. Calculate the threshold frequency (v0) of the metal.

(D) BOHR’S MODEL FOR HYDROGEN ATOM113. Why are Bohr’s orbits called stationary states?114. What do you mean by saying that energy of the electron is quantized?115. The ionization enthalpy of hydrogen in excited state is +0.85eV. What will be the energy of the

photon emitted when it returns to the ground state?116. Which state of triply ionized beryllium (Be3+) has the same orbital radius as that of the ground state

of hydrogen atom?117. Why is electronic energy negative? Comment on the spacing between the energy levels.118. How much energy is required to ionize a hydrogen atom if the electron occupies n = 5 orbit?

Compare your answer with the ionization enthalpy of hydrogen atom (energy required to remove the electron from (n = 1 orbit).

(NCERT)119. What is the maximum number of emission lines when the excited electron of a hydrogen atom in n

= 6 drops to the ground state? (NCERT)

120. (a) The energy associated with the first orbit in the hydrogen atom is –2.18 × 10 –18 J atom–1. What is the energy associated with the fifth orbit? (NCERT)

121. (ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.122. Calculate the wave number for the longest wavelength transition in the Balmer series of atomic

hydrogen (NCERT).

123. What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10-11 ergs. (NCERT)

124. The electron energy in hydrogen atom is given by

En = −2.18×10−18

n2J

Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition? (NCERT)

125. What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He+ spectrum? (NCERT)

126. Calculate the energy required for the processHe+ (g) → He2+ (g) + e-

Given the ionization enthalpy for the hydrogen atom in the ground state is 2.18 × 10–18 J atom–1.

(NCERT)127. Calculate the wavelength for the emission transition if it starts from the orbit having radius 1.3225

nm and ends at 211.6 pm. Name the series to which this transition belongs and the region of the spectrum.

(NCERT)

128. (a) Calculate the radii of the first three Bohr orbits for hydrogen. (Planck’s constant h = 6.626 × 10-

34J s, mass of electron me = 9.1 × 10-31 kg, charge on electron e = 1.602 × 10-19C, permittivity of vacuum ε0 = 8.854 × 10-12 kg-1m-3A2.(b) Use these radii to calculate the velocity of an electron in each of these three orbits.

129. Which of the following species does the Bohr theory apply to?(a) H (b) H+ (c) He (d) He+ (e) Li (f) Li+ (g) Li+2

(h) Be (i) Be+ (j) Be2+ (k) Be3+

130. Ionization enthalpy of a hydrogen atom is 13.6 eV atom -1. It requires a photon of 1.5 times the minimum energy which is required to remove the electron. Calculate the wavelength of the emitted electron.

131. Calculate the radius of the first orbit of electron in an atom of hydrogen.132. What is the experimental evidence in support of the idea that electronic energies in an atom are

quantized?133. What is the difference between ground state and excited state?134. Why is the number of lines observed in the hydrogen spectrum very large?135. Which two discoveries put strong challenge to the Bohr model?136. An electron in a certain Bohr orbit has velocity 1/275 of the velocity of light. In which orbit, is the

electron revolving?137. Write the expression which gives the energy of electron in the nth shell of hydrogen-like particles.138. What is the Bohr frequency condition?139. Calculate the mass of a photon of wavelength 3.6Ǻ.140. What is photoelectric effect? How does particle nature of light explain this effect?141. How does Bohr model explain the appearance of emission spectrum of hydrogen?142. What are the limitations of Bohr’s model of atom?143. Briefly describe Bohr’s theory of the hydrogen atom. How does it differ from the concepts of

classical physics?144. How does de Broglie’s relationship account for the fact that energies of electron in hydrogen atom

is quantized?

145. In hydrogen atom, the energy of electron in the nth orbit is given asEn=−13 .6

n2eV

. Show that

E(n+1 )−En=13. 6×2

n3eV

for large values of n.146. If the energy of an electron in third Bohr orbit is -E, what is the energy of the electron in (a) first

Bohr orbit and (b) second Bohr orbit?147. The angular momentum of an electron in Bohr’s orbit of hydrogen atom is 4.22 × 10 -34 kg m2 s-1.

Calculate the wavelength of the spectral line when the electron falls from this level to the next lower level.

148. The atomic spectrum of hydrogen is found to contain a series of lines at wavelengths 656.46, 486.27, 434.17 and 410.29 nm. What will be the wavelength of the next line in the series?

149. The wavelength of Hα line of Balmer series is 6500Ǻ. What is the wavelength of Hβ line of Balmer series?

150. Find out the quantum number “n” corresponding to the excited state of He+ ion if on radiations to the ground stat that ion emits only two photons in succession with wave length 1026.7Ǻ and 304Ǻ.

(E) TOWARDS QUANTUM MECHANICAL MODEL OF THE ATOM151. The effect of uncertainty principle is significant only for motion of microscopic particles and is

negligible for the macroscopic particle. Justify the statement with the help of a suitable example.152. Why was a change in the Bohr model of atom required? Due to which important development(s),

concept of movement of an electron in an orbit was replaced by the concept of probability of finding electron in an orbital? What is the name given to the modified model of atom?

153. An electron beam after hitting a nickel crystal produces a diffraction pattern. What do you conclude?

154. Prove that if the uncertainty in position of a moving electron is equal to its de Broglie wavelength, then its velocity is completely uncertain.

155. The energy of α – particle is 6.8 × 10-18J. What will be the wavelength associated with it?156. Calculate the wavelength of an electron moving with a velocity of 2.05 × 107ms-1.157. The mass of an electron is 9.1 × 10-31kg. If its kinetic energy is 3.0 × 10-25J, calculate its wavelength.158. Show that the circumference of the Bohr’s orbit for the hydrogen atom is an integral multiple of the

de Broglie wavelength associated with the electron revolving around the orbit.159. Dual behavior of matter proposed by de Broglie led to the discovery of electron microscope often

used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is 1.6 × 106 ms-1, calculate de Broglie wavelength associated with this electron.

(NCERT)160. Similar to electron diffraction, neutron diffraction microscope is also used for the determination of

the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with it.

(NCERT)161. What is the relationship between wavelength and momentum of a particle?162. What is the most important application of de Broglie concept?163. Why does a car not seem to travel in the form of a wave although de Broglie relation is applicable to

it?164. Why did Heisenberg replace the concept of definite orbits by the concept of probability?165. Explain the statement that matter and radiation have a dual nature.166. In what ways does Heisenberg’s uncertainty principle contradicts the concept of stationary orbit for

electron as suggested by Bohr?167. Explain why Heisenberg’s principle is only meaningful for particles such as electrons and atoms

and not for the macroscopic objects.168. Calculate the accelerating potential that must be applied on a proton beam to give it an effective

wavelength of 0.005 nm.169. With what velocity must an electron travel so that its momentum is equal to that of a photon of

wavelength 560 nm?170. (a) Derive the relationship between the wavelength associated with a moving particle and its kinetic

energy. How is the frequency of the matter wave related to the kinetic energy of the particle?

171. Based on Heisenberg’s uncertainty principle, show that electron cannot exist within the atomic nucleus.

172. Calculate the speed and de Brogue wavelength of an electron that has been accelerated by a potential difference of 500 V.

173. Calculate the wavelength of electron moving with one-third velocity of light.

(F) QUANTUM MECHANICAL MODEL OF ATOM174. What is the maximum number of electrons that can be present in an atom in which the highest

principle quantum number is 4?175. Why is Hund’s rule called rule of maximum multiplicity?176. The 4f subshell of an atom contains 10 electrons. What is the maximum number of electrons having

spin in the same direction?177. Do atomic orbitals have sharp boundaries? Explain why or why not.178. Which quantum number does not follow from the solution of Schrödinger wave equation?179. What shell would be the first to have a g subshell? How many orbitals will be possible in a g

subshell?180. What is the angular momentum of an electron in (a) 2s orbital (b) 4f orbital?181. Out of Cu2+, Fe2+, and Cr3+, which ion is most paramagnetic and why?182. What physical meaning is attributed to the square of the absolute value of wave function, |ψ |2?183. What is the maximum probability for an electron to be present within the atomic orbital?184. One unpaired electron in an atom contributes a magnetic moment of 1.1 BM. Calculate the magnetic

moment for chromium.185. At what distance is the radial probability maximum for 1s orbital? What is the distance called?186. Discuss the similarities and differences between a 1s and a 2s orbital.187. How many radial/spherical nodes will be present in the 5f orbital?188. What is the deviation from the Aufbau principle in the case of electronic configuration of La (Z =

57)?189. What is the difference between the notations l and L?190. How many orbitals do you expect to be present in the fifth shell?191. Which of the following are the isoelectronic species, that is, those having the same number of

electrons? (NCERT)

192. (a) Write the electronic configurations of the following ions: (i) H+ (ii) Na+ (iii) O2– (iv) F–

193. (b)What are the atomic numbers of elements whose outermost electrons are represented by (i) 3s 1, (ii) 2p3 and (iii) 3d6?

194. (iii) Which atoms are indicated by the following configurations: (i) [He] 2s 1 (ii) [Ne] 3s2 3p3 (iii) [Ar] 4s2 3d1.

(NCERT)195. What is the lowest value of n that allows g orbitals to exist?

(NCERT)

196. An electron is one of the 3d orbitals. Give the possible values of n, l and ml for this electron.

(NCERT)

197. An atom of an element contains 29 electrons and 35 neutrons. Deduce (i) the number of protons and (ii) the electronic configuration of the element. (NCERT)

198. Give the number of electrons in the species H2+, H2 and O2+. (NCERT)

199. (i) An atomic orbital has n = 3. What are the possible values of l and ml?(ii) List the quantum numbers (ml and l) of electrons for 3d orbital.(iii) Which of the following orbitals are possible?

1p, 2s, 2p and 3f (NCERT)

200. Using s, p, d notations, describe the orbital with the following quantum numbers.(a) n = 1, l = 0; (b) n = 3; l = 1 (c) n = 4; l = 2; (d) n = 4; l = 3. (NCERT)

201. Explain, giving reasons, which of the following sets of quantum numbers are not possible.(a) n= 0 l = 0 ml = 0 ms = + ½ (b) n = 1 l = 1 ml = 0 ms = - ½ (c) n = 2 l = 2 ml = 0 ms = + ½

(d) n = 3 l = 3 ml = 0 ms = - ½ (e) n = 4 l = 4 ml = -3 ms = + ½

(f) n = 5 l = 5 ml = 0 ms = + ½

202. How many electrons in an atom may have the following quantum numbers?(a) n = 4, ms - ½ (b) n = 3, l = 0 (NCERT)

203. The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/have the same energy.

(NCERT)(a) n = 4, l = 2, ml = –2 , ms = –1/2 (b) n = 3, l = 2, ml = 1 , ms = +1/2(c) n = 4, l = 1, ml = 0 , ms = +1/2 (d) n = 3, l = 2, ml = –2 , ms = –1/2(e) n = 3, l = 1, ml = –1 , ms = +1/2 (f) n = 4, l = 1, ml = 0 , ms = +1/2

204. The bromine atom possesses 35 electrons. It contains 6 electrons in 2p orbital, 6 electrons in 3p orbital and 5 electron in 4p orbital. Which of these electron experiences the lowest effective nuclear charge?

(NCERT)

205. Among the following pairs of orbitals which orbital will experience the larger effective nuclear charge? (i) 2s and 3s, (ii) 4d and 4f, (iii) 3d and 3p. (NCERT)

206. The unpaired electrons in Al and Si are present in 3p orbital. Which electrons will experience more effective nuclear charge from the nucleus? (NCERT)

207. Indicate the number of unpaired electrons in: (a) P, (b) Si, (c) Cr, (d) Fe and (e) Kr.208. (a) How many sub-shells are associated with n = 4?

(b) How many electrons will be present in the sub-shells having ms value of –1/2 for n = 4?209. How does the Bohr theory of the hydrogen atom differ from that of Schrödinger?

210. (a) Write down the general form of the Schrödinger equation and define each of the terms in it.(b) What does each solution of the wave equation correspond to and what are the set of numbers that describe it?

211. Explain (a) the Pauli’s exclusion principle and (b) Hund’s rule. Show these are used to specify the electronic arrangements of the first 20 elements in the periodic table.

212. Give the notation for subshells denoted by the following quantum numbers: (a) n = 6, l = 2; (b) n = 4, l = 3; (c) n = 4, l = 2 and (d) n = 5, l = 4.

213. What kind of information about an electron in an atom is obtained from its wave function?

214. What is an orbital? Draw the shapes of the 1s, 2s, 2px, 2py, 2pz, 3dxy, 3dyz, 3dx2-y2 and 3dz2

orbitals.215. What are the two properties of orbitals in which we are most interested? Why?216. How does the size of a given type of orbital vary with n.217. Within any given shell, how do the energies of the s, p, d and f subshells compare? What fact about

the energies of subshells was responsible for the apparent success of Bohr’s theory about electronic structure?

218. Give the names and symbols of the four quantum numbers required to define the energy of electrons in atoms. What do these quantum numbers relate to, and what numerical values are possible for each? Show how the shape of the periodic table is related to these quantum numbers.

219. The first shell may contain up to 2 electrons, the second shell up to 8, the third shell up to 18, and the fourth shell up to 32. Explain this arrangement in terms of quantum numbers.

220. If a transition from an upper level to n = 1 in hydrogen spectrum results in light of wavelength 9.50 × 10-8m-1 in being emitted, what is the principle quantum number of the higher level?

221. Give the values of the four quantum numbers for each electron in the ground state for (a) the oxygen atom, and (b) the scandium atom. (Use positive values for ml and ms first.)

222. Give the sequence in which the energy levels in an atom are filled with electrons. Write the electronic configurations for the elements of atomic number 6, 11, 17 and 25, and from this decide to which group in the periodic table each element belongs.

223. Give the name and symbol for each of the atoms which have the ground state electronic configurations in their outer shells:

(a) 2s2 (b) 3s23p5 (c) 3s23p64s2

(d) 3s23p63d64s2 (e) 5s25p2 (f) 5s25p6

224. Which of the following orbitals are degenerate?3dxy, 4dxy, 3dz2, 3dyz, 4dyz, 4dz2

225. Calculate the total number of angular nodes and radial nodes present in 3p orbital.226. The wave function of 2s electron is given by

Ψ2s =

14√2 π ( 1

a0)

32 (2− r

a0)e

− ra0

It has a node at r = r0. Find the relation between r0 and a0.227. How many nodes are present in 3p – orbital? Represent diagrammatically.228. In each of the following pairs of salts, which one is more stable?

(a) Ferrous and ferric salts(b) Cuprous and cupric salts.229. Which orbital does not have directional characteristic?230. Which quantum number determines the (a) shape, (b) orientation and (c) size of the orbital?

s orbital p orbital

231. Which energy level does not have a p orbital?232. Which is the first energy level containing f orbitals?233. Which element has only one electron in the d orbital?234. Which quantum number tends to specify the orientation in space for an orbital?235. What are degenerate orbitals?236. What does angular momentum quantum number tell about an orbital?237. Write a neutral molecule which is isoelectronic with CIO-.238. What is the physical significance of the lines in the following depictions of atomic orbitals?

239. Based on Pauli’s exclusion principle, show that the maximum number of electrons in the subshells with n = 3 of any individual atom is 18.

240. What is the significance of wave function ψ in the Schrodinger wave equation? What is an atomic orbital? Why ψ is called orbital wave function?

241. Describe the four quantum numbers that characterize an electron in an atom.242. Define Pauli’s exclusion principle. What is the total number of electrons that can be held in all

orbitals having the same principal quantum number?243. Write electronic configurations of atoms of Cr (atomic number 24) and Cu (atomic number 29).

Show the orientations of electron spins by arrow heads.244. What is electronic configuration? Why do some atoms possess exceptional electronic configuration?

Give two examples.245. (a) Explain how the study of quantum numbers led to Pauli’s exclusion principle?

(b) Compare and contrast the characteristic features of 1s and 2s orbitals.246. What do you understand by quantum numbers? Briefly explain significance of each of them.247. Describe the shapes of s, p and d orbitals and relate them to quantum numbers n, l and m1.248. List the main features of the quantum mechanical model atom.