P Kenny Lecture Notes

8/2/2019 P Kenny Lecture Notes

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Chemistry

CS214, CS108, FSH104

P. T. M. Kenny


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Atoms are made up of sub-atomic particles. Chemists only need to know about electrons,

protons and neutrons, (we will leave a fuller description of what these sub atomic particles are

made of to nuclear physics!). Both protons and neutrons have a mass of 1 atomic mass unit(approximately) and electrons have negligible mass. The structure of the atom places most of its

mass in a small volume of space called the nucleus.

.

The periodic table of the elements contains information on the known elements, including a

chemical symbol (which sometimes helps us to remember its name) and other parameters which

can tell us something about the relative masses of the atoms of the element and an indication of

its likely chemistry. As most of the mass of an atom comes from the protons and neutrons in the

atom, the atomic mass of an atom is the sum total of the protons and neutrons in the nucleus.

As chemists we are also interested in the electronic structure of the atom and would like

to know the number of electrons in the atom. To maintain electrical neutrality the

number of protons must equal the number of electrons, so for the electrically neutral

atom the atomic number tells us how many protons there are in the nucleus and how

many electrons are orbiting the nucleus. Chemists are good at manipulating the

electrons in atoms, but tend not to meddle with the nucleus very often, so in generating

ions (species with an electrical charge) we change the number of electrons orbiting the

nucleus and leave the number of protons unchanged. We remove electrons to form

positive ions (cations) and add electrons to produce negative ions (anions).

The chemical properties of an atom are controlled by the number of electrons. To maintain electrical

neutrality the number of electrons must equal the number of protons. It is possible, however, that in

E

AtomicNumber

AtomicMass

y

xElement

Symbol


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a particular element, the number of neutrons can vary. We can think of neutrons as the glue that

holds the nucleus together.

Electromagnetic radiation (of which light is a part) consists of oscillating electric and magnetic

fields.

Electromagnetic radiation can be classified either by its wavelength (measured in

metres) or by its frequency measured in 1/s or s-1 (called Hertz).

When we discuss the properties of light we must remember one important fact, namely

the velocity (speed) of light in a particular medium is constant. This constant is given

the symbol c for the velocity of light in a vacuum (approximately 3.00 108 ms-1).


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c=

So using this equation we can calculate the frequency of light if we know its wavelength and visa

versa. For example what is the frequency of visible light with a wavelength of 4 10-7 m?

7

8

104

103

=m

ms1

Check the dimensions! Is the unit for frequency correct?

Answer = 147.5 10 s-1

Check that this number is of the right order according to the spectral information provided in the

diagram above.

What is the frequency of light with a wavelength of 0.53m? What region of the spectrum does this

photon belong?

The energy of a photon depends on its frequency. Because the frequency is also related to the

wavelength of the photon, the energy also depends on the wavelength. The energy of a photon is

directly proportional to the frequency

E The constant of proportionality is called Plancks constant and given the symbol h and has a value

of 6.63 10-34 J s. So Plancks equation becomes

E h =

If we know the frequency of a photon we can calculate its energy, and if we know the energy we

can calculate the frequency. Also because we can relate the frequency to wavelength as we saw in

the last question, we can rewrite Planks equation in terms of wavelength.


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hcE

=

(Check to see if the dimensions are correct for energy!)

Which of the following has the shortest wavelength; X-ray, radio or infrared light? (Look at the

diagram of the electromagnetic spectrum given above).

Because we know that the velocity of light is constant we can relate the frequency of light and its

wavelength. We can also relate the energy to frequency using Plancks equation. Consequently we

can relate the energy of a photon to the wavelength as we have seen before:

hcE

=

Using this equation calculate the wavelength of radiation that corresponds to a photon of energy of

3.31 x 10-20 J?


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The Bohr model of an atom places the nucleus at the centre with electrons orbiting the nucleus in

specific energy levels. The energy of the energy levels is described by the principle quantum

number of the energy level. These principle quantum numbers are given the symbol n, and can have

only integer values (n = 1, 2, 3, 4..).

If an electron moves from on orbital to an orbital of higher energy it must receive a packet

(quantum) of energy exactly equal to the energy difference between the energy levels. Likewise if

an electron moves to an energy level of lower energy it must emit a quantum of energy exactly

equal to the energy difference between the initial and final energy levels.

The energies of transitions were explained using an empirically derived equation known as the

Rhydberg equation. Bohr subsequently provided a theoretical basis for this equation now known as

the Bohr equation. Both equations are the same, except for the units of the BH (sometimes called RH

for the Rhydberg equation) the subscript H signifying the hydrogen atom. The equation is as

follows:

Where B is the Bohr constant for the

atom (for the hydrogen atom the value (BH) is 2.179

10-18

J)

, nf is the quantum number of

final energy level and ni is the quantum number of the initial energy level.

According to Einstein the energy associated with matter is expressed according to his famous

equation

where m is the mass of the matter and c is the velocity of light. For a photon the energy is defined

by its frequency or wavelength

hcE

=

2 2 2 2

1 1H HH

i f i f

B BE B

n n n n

= =

2E mc=


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By treating matter as an electromagnetic wave we can equate these two equations

2 hcmc

=

which simplifies to

hmc

=

Rearranging this equation gives

Assuming this equation holds for all velocities (not true but lets assume it is) we

can rewrite this for the general velocity v

h

mv=

So if we know Plancks constant (6.63 10-34 kgm2s-1) and the mass (m) and velocity (v) of the

object we can calculate a nominal wavelength.

Which quantum number determines the energy of an electron in a hydrogen atom, (n, m l, or l)?

How many quantum numbers are required to designate a particular orbital in an atom?

The first (principal) number is the energy quantum number, n can have integer values i.e. 1,2,3,

.etc. The second quantum number is called the azimuthal quantum number, l (small L). The

azimuthal quantum number, l, defines the shape of the orbital. l can have numbers based on the

value of n thus l= 0,1,2,(n-1). The orbitals associated with the various values of l are given the

letters, s (l=0), p (l=1), d (l=2), and finally f (l=3). The third quantum number is the magnetic

quantum number ml. This quantum number defines the orientation of the orbital. The possible

values of ml is determined by the value of l, such that ml= l, l-1, l-2, .0.-l. So for l = 2 ml = 2,

1, 0, -1,-2. In addition to these three quantum numbers there is a fourth, known as the spin quantum

number, ms. ms can have a value either + or -

h

mc=


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9.

In the following sets of quantum numbers for electrons, indicate those which could occur, and the

names of the orbitals for those which cannot occur:

n l ml ms

a) 2 0 0 - 1/2

b) 1 0 2 + 1/2

c) 3 -1 -1 + 1/2

d) 3 1 -1 -1/2

e) 3 2 0 0

The atomic orbitals are filled in a specific order depending on their energies, which because of

electron-electron repulsion factors do not follow the strict order of the energy quantum number.

The following diagram gives the order in which the orbitals are filled.

Slaters rules help us to predict how much of the charge on the nucleus, certain specific electrons

will see. This is called the Effective Nuclear Charge ENC.

Z* = Z - s


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Where Z* is the ENC Z is the actual nuclear charge and s is a screening constant.

Step 1

Write down the electron configuration of the element

1s 2s 2p 3s 3p 3d 4s 4p 4d

Step 2

Group the orbitals as follows

(1s) (2s 2p) (3s 3p) (3d) (4s 4p) (4d)

Step 3

Select the electron of interest

Step 4

Electrons to the right of the selected electron contribute nothing to the screening

constant

Step 5

All other electrons in the same orbital group contribute 0.35 (0.3 for 1s)

Step 6

All electrons in the group immediately to the left contribute 0.85

Step 7

All electrons in groups further to the left contribute 1.0

Step 8

For d or f electrons, electrons in the same group contribute 0.35, and all electrons in

groups to the left contribute 1.00.

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P Kenny Lecture Notes