Quantum numbers (4)

1. Principal quantum number, n

2. Angular momentum quantum number, l

3. Magnetic quantum number, m_{l}

4. Spin quantum number, m_{s}

Principal quantum number

n

Indicates the orbital (Bohr's energy level)

*As n gets larger, amount of energy between orbitals gets smaller

Equation for energy of a hydrogen electron

**E _{n} = -R_{H} (1/n^{2})**

R_{H} is Rydberg constant for hydrogen

R_{H} = 2.18 × 10^{-18} J

Angular momentum quantum number

l

Angu**l**ar momentum = what kind of/angle of orbit

**l =** 0, 1,... **n-1**

l = 0 → s

l = 1 → p

l = 2 → d

l = 3 → f

e.g.

n = 2

l = [0, 1]

Magnetic quantum number

m_{l}

**m _{l} = [-l, l]**

e.g.

n = 2

l = [0, 2] → d orbital

m_{l} = [-2, 2] → 5 d orbitals

Spin quantum number

**m _{s}**

Specifies the orientation of the spin of the electron

Value is either:

+1/2 (spins up)

or

-1/2 (spins down)

Describing an orbital (3)

1. n, l, m_{l} describes one orbital

2. Orbitals with same **n** value = same **principal energy level** (shell)

3. Orbitals with the same values of **n & l** = same **sublevel** (subshell)

Equation for energy transition in hydrogen

ΔE = E_{final} - E_{initial}

**ΔE _{H atom} = -2.18 × 10^{-18} J (1/n^{2}_{final} - 1/n^{2}_{initial})**

Energy emitted by electron is carried away by the releated photon, thus:

**E _{photon} = -ΔE**

Probability density

The probability of finding an electron at a **particular** **point** in space

Probability decreases as distance from nucleus increases

Radial distribution function

**Total probability** of finding an electron at a **certain** **distance** *r* from the nucleus

Volume of shell also increases with distance from nucleus

Nodes

Where the probability drops to zero, for both probabilities

s orbital

l = 0

spherical shape

1 s orbital

p orbital

l = 1

shaped like two balloons

-1, 0, 1

3 p orbitals

d orbital

l = 2

shaped like four balloons

-2, -1, 0, 1, 2

5 d orbitals

f orbital

l = 3

shaped like eight balloons

-3, -2, -1, 0, 1, 2, 3

7 f orbitals