1) What is the surface temperature of (a) Betelgeuse, a red giant star in the constellation of Orion, which radiates with a

peak wavelength of about 970nm? (b) Rigel, a bluish-white star in Orion, radiates with a peak wavelength of 145nm. Find

the temperature of Rigel's surface.

a) maxT = 0.2898x10-2 mK => T = 0.2898x10-2 mK/max =>

=> T = 0.2898x10-2 mK/(970x10-9m) => T = 3x10-4 x 107 K =>T = 3000 K

b) maxT = 0.2898x10-2 mK => T = 0.2898x10-2 mK/max =>

=> T = 0.2898x10-2 mK/(145x10-9m) => T = 2x10-3 x 107 K =>T = 20,000 K

3) The average surface temperature of the Sun is 5,800 K. What wavelength light is the most intensely emitted? Compare

3) The average surface temperature of the Sun is 5,800 K. What wavelength light is the most intensely emitted? Compare

your result with the green light having wavelength 560-nm which is the light the human eye is most sensitive to.

maxT = 0.2898x10-2 mK => max = 0.2898x10

-2 mK/T=>

=> max = 0.2898x10-2 mK/(5800K) => max = 5x10

-5 x 10-2 m

=> max = 5x10-7 m = 500 nm

The most intensely emitted color is greenish. However the blend of all colors makes the sun yellowish white.

7) An FM radio transmitter has a power output of 150 kW and operates at a frequency of 99.7 MHz. How many photons per

second does the transmitter emit?

11) When light of wavelength 350 nm falls on a potassium surface, electrons having a maximum kinetic energy of 1.31 eV

are emitted. Find (a) the work function of potassium, (b) the cutoff wavelength, and (c) the cutoff frequency. Recall that

1eV = 1.6 x 10-19 j.

a) Ephoton = hf = hc/ = 6.63 x 10-34 x 3 x 108 /(350 x 10-9) =

0.0568 x 10-17 j =

= 0.0568 x 10-17 / (1.6 x 10-19 ) eV = 0.0355 x 102 eV=> Ephoton = 3.55 eV

Ephoton = f + KEmax => 3.55 = f + 1.31 => f = 2.24 eV =

2.24x1.6x10-19 j = 3.584x10-19 j

b) cutoff = hc/f => cutoff = 6.63 x 10-34 x 3 x 108 /(3.584 x

10-19) =>

=> cutoff = 5.55 x 10-7 m => cutoff = 555 nm

The photoelectric effect occurs for light wavelengths equal or smaller than the cutoff wavelength.

c) fcutoff = f/h => fcutoff = 3.584x10-19/6.63 x 10-34 => fcutoff

= 5.41x1014 Hz

The photoelectric effect occurs for light frequencies equal or greater than a cutoff frequency.

Second Method:

c= f => fcutoff = c/cutoff => fcutoff = 3 x 108 / 555x10-9 =>

fcutoff = 5.41x1014 Hz

12) When a certain metal is illuminated with light of frequency 3.0 x 1015 Hz, a stopping potential of 7.0 V is required to

stop the most energetically ejected electrons. What is the work function of the metal? What is the cutoff frequency?

13) What wavelength of light would have to fall on sodium (with work function of 2.46 eV) if it is to emit electrons with a

max speed of 1.0x106 m/sec?

30) X-rays with an energy of 300 keV undergo Compton scattering from a target. If the scattered rays are deflected at 370

relative to the direction of the incident rays, find (a) the Compton shift at this angle, (b) the energy of the scattered x-

ray, and (c) the kinetic energy of the recoiling electrons.

34) Calculate the de Broglie wavelength of a proton moving at a) 2.00x104 m/sec b) 2.00x107 m/sec.

35) (a) If the wavelength of an electron is 5.00 x 10-7 m, how fast is it moving? (b) If the electron has speed of 1.00 x 107

m/s, what is its wavelength?

36) A 0.200-kg ball is released from rest at the top of a 50.0-m tall building. Find the de Broglie wavelength of the ball just

before it strikes the Earth. Assume no air resistance.

41) The resolving power of a microscope is proportional to the wavelength used. A resolution of 1.0 x 10-11 m (0.010nm)

would be required in order to "see" an atom (if we use light to see the atom, what we really see is the flash of light

scattered by the atom). (a) if electrons were used (electron microscope), what minimum kinetic energy would be

required of the electrons? (b) If photons were used, what minimum photon energy would be needed to obtain 1.0 x 10 -11

m resolution?

42) A 50.0-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.10%, what is the minimum uncertainty in

its position?

44) Suppose Fuzzy, a quantum mechanical duck, lives in a world in which h = 2 j x s. Fuzzy has a mass of 2.00 kg and is

initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in his speed? (b) Assuming this

uncertainty in speed to prevail for 5.00 s, determine the uncertainty in Fuzzy's position after this time.

Extra (similar to problem 46): Redo this problem by assuming Fuzzy is an electron in the hydrogen atom. For this case use

realistic numbers. That is, h = 6.63x10-34 j sec, the mass of the electron is 9.11x10-31kg, the "size" of the hydrogen atom

(in its ground state - see lesson 10) is about 10-11m.

45) Suppose optical radiation (= 5.00 x 10-7 m) is used to determine the position of an electron to within the wavelength

of the light. What will be the resulting uncertainty in the electron's velocity.

of the light. What will be the resulting uncertainty in the electron's velocity.

8) Suppose an electron is found to be somewhere in an atom of diameter 1.25 x 10-10 m. a) Estimate the uncertainty in the

electron's momentum in 1-d. b) Estimate the uncertainty in the electron's velocity in 1-d.

a) DxDp h/4p => Dp h/(4pDx) => Dp (6.63x10-34)/(4p

1.25x10-10) =>

=> Dp 4.22 x 10-25 (kg m)/sec

b) Dp 4.22 x 10-25 => mDv 4.22 x 10-25 => Dv 4.22 x 10-

b) Dp 4.22 x 10-25 => mDv 4.22 x 10-25 => Dv 4.22 x 10-

25/m =>

=> Dv 4.22 x 10-25/(9.11x10-31) => Dv 0.463 x 106 => Dv

4.63 x 105 m/sec

The smaller the region Dx a particle is confined the faster it moves to get awayfrom it. This is a useful concept to understand Pauli's exclusion principle which isintroduced next lesson.

46) a) Show that the kinetic energy of a non-relativistic particle can be written in terms of its momentum as KE = p2/2m.

b) Use the result of a to find the minimum kinetic energy of a proton confined within a nucleus having a diameter of

1.0x10-15 m.