Modern Physics

One exciting thing from modern physics is the glow-in-the-dark Frisbee.

Key Things to Know in Modern Physics

Light waves can behave like a particle. This behavior is observed in photoelectric effect experiments.
Particles can behave like a wave as seen in electron diffraction experiments.
Light particles are called photons.
Strong nuclear force hold protons together in a nucleus.
When an atom absorbs photon, the electron jumps from a lower energy level to a higher energy level.
The difference between the lower energy level and the higher energy level is equal to the energy of the absorbed photon.
When an atom releases energy in the form of a photon, electron falls from a higher energy level to a lower energy level.
The difference between the lower energy level and the higher energy level is equal to the energy of the emitted photon.
An atom absorbs or emits photons with energy exactly equal to the difference between two energy levels of the atom.

Key Words in Modern Physics

Energy level, Photon, Quarks, Strong Nuclear Force (strong force), ground state, antiparticle

Energy level: the amount of energy that an atom has.
Photon: light particle.
Quarks: smaller particles that combine to form more stable particles like protons and neutrons
Strong nuclear force: the force that holds protons together in a nucleus of an atom.
Ground state: the lowest energy state of a atom.
Antiparticle: has a charge opposite to its associated particle

Formula in Modern Physics

E = mc²
E_photon = hf
E_photon = ΔE = E_i - E_f

Example 1

Q: An electron in a mercury atom changes from energy level b to a higher energy level when the atom absorbs a single photon with an energy of 3.06 electronvolts.
a) Determine the letter that identifies the energy level to which the electron jumped when the mercury atom absorbed the photon.

E = E_b + E_photon = -5.74 eV + 3.06 eV = -2.68 eV = E_f. The energy level is f.

b) Determine the energy of the photon, in joules.

E_photon = 3.06 eV (1.6 × 10^-19 J)/(1 eV) = 4.896 × 10^-19 J

c) Calculate the frequency of the photon.

E_photon = hf
f = E_photon/h = (4.896 × 10^-19 J)/(6.63 × 10^-34 J·s) = 7.38 × 10¹⁴ Hz

d) Classify the photon as one of the types of electromagnetic radiation listed in the electromagnetic spectrum.

Violet visible light because 6.59 × 10¹⁴ Hz < f < 7.69 × 10¹⁴ Hz

Example 2

Q: What is the total energy produced by converting 1.0 kilogram of Uranium-235 to energy?

E = mc² = 1kg × (3 × 10⁸ m/s)² = 9 × 10¹⁶ J

Example 3

Q: An electron in a hydrogen atom drops from the n = 3 energy level to the n = 2 energy level.
a) What is the energy of the emitted photon?

E_photon = E_larger - E_smaller = 3.4 eV - 1.51 eV = 1.89 eV
E_photon = 1.89 eV (1.6 × 10^-19 J)/(1 eV) = 3.024 × 10^-19 J

b) What is the color of the photon?

E_photon = hf
f = E_photon/h = (3.024 × 10^-19 J)/(6.63 × 10^-34 J·s) = 4.56 × 10¹⁴ Hz
Red color in the visible light spectrum because 3.84 × 10¹⁴ Hz < f < 4.82 × 10¹⁴ Hz

C) Describe how an atom emits a photon.

When an electron in an atom falls to a lower energy level, the atom gives off a photon with energy equal to the difference between the two energy levels.

Example 4

Compared to the wavelength of red light,
the wavelength of yellow light is
1) shorter
2) longer
3) the same

On p. 2 of the reference table, red color has f = 4E14 Hz for example and yellow has f = 5E14 Hz.
On p. 5 of the reference table, v = f λ. Since v = fixed = 3E8 m/s. As color changes from red to yellow, the frequency increases. This means the wavelength λ has to decrease. Therefore, the yellow has a shorter wavelength.

Exercises

1. Compared to the energy of red light,
the energy of yellow light is
1) less
2) greater
3) the same

2. A photon of light carries
1) energy, but not momentum
2) momentum, but not energy
3) both energy and momentum
4) neither energy nor momentum

3. Experiments performed with light indicate
that light exhibits
1) particle properties, only
2) wave properties, only
3) both particle and wave properties
4) neither particle nor wave properties

4. How much energy is required to move an
electron in a mercury atom from the
ground state to energy level h?

5. What is the energy equivalent of 5.0 × 10^-3 kilogram?