Modern
Physics

**Momentum
of a Photon**

(5)

**Example
8**

Calculate
the momentum of a photon of yellow light with a frequency of .

Solution:

**Compton
Effect**

**Compton
Shift Formula**

(6)

**Example
9**

An
X-ray photon with a wavelength of 0.650 nm scatters from a free
electron at rest. After scattering, the photon moves at an angle
of 152° relative to the incident direction. Find (a) the
wavelength and (b) the energy of the scattered photon. (c) Determine
the kinetic energy of the recoiling electron.

Solution:

(a)

(b)

(c)

**De
Broglie Waves**

(7)

**Example
10**

How
fast is an electron moving if its De Broglie wavelength is ?

Solution:

**Energy Level Diagrams**

Bohr
Energy Levels in Joules:

(8)

Bohr
Energy Levels in Electron Volts:

(9)

Example
11

An energy-level diagram for a hypothetical atom is
shown above.

a. Determine the frequency of the lowest energy photon that could
ionize the atom, initially in its ground state.

b. Assume the atom has been excited to the state at -1.0 electron
volt.

i. Determine the wavelength of the photon for each possible spontaneous transition.

ii. Which, if any, of these wavelengths are in the visible range?

c.
Assume the atom is initially in the ground state. Show on the
following diagram the possible transitions from the ground state
when the atom is irradiated with
electromagnetic radiation of wavelengths ranging continuously from meter
to meter.

Solution:

(a)

(b)

i

ii
Two of the energies are in the visible range: 2.0 eV and 2.5
eV.

(c)

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