physicsa.com
 class code: SPS22 teacher: Mr. Elert classroom: A314 office: A214 test day: Friday phone: (718) 724–8500 ext. 2141 email: elert@midwoodscience.org

## Physics A: Problem Set 22: The Particle Nature of Light

 Barron's Let's Review: 13.1–13.4 physics.info: Photoelectric Effect, X-rays Wikipedia: Photoelectric effect, Photon, X-ray HyperPhysics: Photoelectric Effect, Wave-Particle Duality Khan Academy: Photoelectric effect

### in class

1. Complete the following table for photons of visible light.
λmax λmed λmin
wavelength (nm) 700 nm 550 nm 400 nm
frequency (Hz)
energy per photon (J)
energy per photon (eV)
color
λmax λmed λmin
wavelength (m) 700 nm 550 nm 400 nm
frequency (Hz) 4.28 × 1014 Hz 5.45 × 1014 Hz 7.49 × 1014 Hz
energy per photon (J) 2.84 × 10−19 J 3.61 × 10−19 J 4.97 × 10−19 J
energy per photon (eV) 1.77 eV 2.26 eV 3.10 eV
color red green violet

Frequency is computed using the wave speed equation and the speed of light in a vacuum (c = 3.00 × 108 m/s).

 f = c ⇐ c = fλ λ

Energy per photon in joules is computed using Planck's relationship and Planck constant (h = 6.63 × 10−34 Js).

E = hf

To convert from joules to electronvolts, divide the energy in joules by the elementary charge in coulombs (q = 1.60 × 10−34 C).

 V = E q

The visible spectrum starts with red and ends with violet when the colors are listed in order of increasing frequency (red, orange, yellow, green, blue, violet). Since frequency and wavelength are inversely proportional, the lowest frequency light (red) goes with the longest wavelength and the highest frequency light (violet) goes with the shortest wavelength and green is in the middle.

2. Complete the following table for different types of electromagnetic radiation.
E1 E2 E3
energy per photon (eV) 100 eV 103 eV 106 eV
energy per photon (J)
frequency (Hz)
wavelength (m)
E1 E2 E3
energy per photon (eV) 100 eV 103 eV 106 eV
energy per photon (J) 1.60 × 10−19 J 1.60 × 10−16 J 1.60 × 10−13 J
frequency (Hz) 2.42 × 1014 Hz 2.42 × 1017 Hz 2.42 × 1020 Hz
wavelength (m) 1.24 × 10−6 m 1.24 × 10−9 m 1.24 × 10−12 m
(ultraviolet)
gamma ray
(x‑ray)

To convert from electronvolts to joules, multiply the voltage in volts by the elementary charge in coulombs (q = 1.60 × 10−34 C).

 E = qV ⇐ V = E q

Frequency is computed using Planck's equation and Planck's constant (h = 6.63 × 10−34 Js).

 f = E ⇐ E = hf h

Wavelength is computed using the wave speed equation and the speed of light in a vacuum (c = 3.00 × 108 m/s).

 λ = c ⇐ c = fλ f

The type of radiation can be found in the spectrum chart of your choice.

3. The Balmer series is a set of wavelengths emitted by excited hydrogen atoms. Complete the following table for the four visible wavelengths in the Balmer series identified by the Greek letters α (alpha), β (beta), γ (gamma), and δ (delta).
α β γ δ
wavelength (nm) 656 nm 486 nm 434 nm 410 nm
frequency (Hz)
energy per photon (J)
energy per photon (eV)
color
α β γ δ
wavelength (nm) 656 nm 486 nm 434 nm 410 nm
frequency (Hz) 4.57 × 1014 Hz 6.17 × 1014 Hz 6.91 × 1014 Hz 7.32 × 1014 Hz
energy per photon (J) 3.03 × 10−19 J 4.09 × 10−19 J 4.58 × 10−19 J 4.85 × 10−19 J
energy per photon (eV) 1.90 eV 2.56 eV 2.86 eV 3.03 eV
color red blue violet violet

Frequency is computed using the wave speed equation and the speed of light in a vacuum (c = 3.00 × 108 m/s).

 f = c ⇐ c = fλ λ

Energy per photon in joules is computed using Planck's relationship and Planck constant (h = 6.63 × 10−34 Js).

E = hf

To convert from joules to electronvolts, divide the energy in joules by the elementary charge in coulombs (q = 1.60 × 10−34 C).

 V = E q

Color is found using your friendly neighborhood reference tables. If you don't have a reference table, I hear there's this thing called Google that can help you find one.

### at home

1. Three related questions.
1. Why are ultraviolet, x-rays, and gamma rays always regarded as harmful while infrared, microwaves, and radio waves are generally regarded as benign (by sensible people, anyway).
2. In what sense can visible light be thought of as "just right" as an energy source for life (and other forms of chemistry) on earth?
3. Under what circumstances could exposure to the generally benign electromagnetic waves listed in part a. be considered harmful?