**Examples for atomic physics**

Example #1

Problem:

True or False:

a.) An electron in the ground state of a Hydrogen atom has zero orbital angular momentum.

b.) An electron in the ground state of a Hydrogen atom has zero spin angular momentum.

c.) An electron in the ground state of a Hydrogen atom has zero kinetic energy.

d.) An electron in the ground state of a Hydrogen atom has zero probability of being at the origin.

e.) An electron in the ** n=2**
level of Hydrogen will emit visible light when it decays to the ground state.

*T,F,F,F,F*

Example #2

Problem:

a.) What is the energy of a photon emitted
as an electron moves from the * n* = 5 to the

Solution:

The energy of each level goes as (13.6 *eV*)/**n**^{2}.
The difference between the * n* = 5 and

2.9 *eV*

b.) What is the wavelength of such a photon?

Solution:

Change the energy to Joules, then use * E*
=

686 *nm*

c.) What is the energy of a photon in the same transition is carbon (Z=6)?

Solution:

The energy scales as **Z**^{2},
so multiply the answer in part * a* by 36.

103* eV*

Example #2

Problem:

a.) How many electrons are in an atom
specified by 1s^{2},2s^{2},2p^{6},3s^{2},3p^{4}?

Solution:

Count up the numbers in the superscripts.

16

b.) Write the spectroscopic notation for a neutral gold (Au) atom?

Solution:

See that a gold atom should have 79 electrons by looking at the periodic table. Then count up:

1s^{2},2s^{2},2p^{6},3s^{2},3p^{6},3d^{10},4s^{2},4p^{6},4d^{10},4f^{14},5s^{2},5p^{6},5d^{10},5f^{1}