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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