Energy, Wavelength and Frequency Calculation Notes and Problems
Formulas:
Variables: What you solve for
E=hƒ
(energy and frequency)
E = Energy of a photon of light
 Unit is Joules (J)
λ = Wavelength
 Unit is Meters (m)
ƒ = Frequency
 Unit is Hertz (Hz)
λƒ=c
(wavelength and frequency)
λ E = hc
(wavelength and energy)
Constants: Always is the same
number!
C = Speed of light
 Always 3x108 m/s
H= Planck’s Constant
 Always 6.6x10-34
Example Problems
What is the frequency of ultra violet radiation that has a wavelength of 4.2x10 -7 meters?
Question:
Formula:
Solution:
λƒ=c
3𝑥108
𝐜
ƒ=𝛌=
(4.2𝑥10−7 )
= 𝟕. 𝟏 𝐱𝟏𝟎𝟏𝟒 𝐇𝐳
How much energy does a photon with the frequency of 6.2x1015have?
Solution: E = h ƒ = (6.6x10-34)( 6.2x1015) = 4.1x10 -18 J
Question:
Formula:
E=hƒ
How much energy does a photon with the wavelength of 4.2x10-7 meters have?
Question:
Formula:
Solution: E =
λ E = hc
hc
𝛌
=
(6.6𝑥10−34 )(3𝑥108 )
(4.2𝑥10−7 )
= 4.7x10-19 J
Practice Problems
14
1. What is the energy of a quantum of light with a frequency of 7.39 x 10 Hz?
E = hf
(6.6x10-34)(7.39x1014) = 4.9x10-19J
2. What is the wavelength of the quantum of light in question 1?
λ=
c
f
3𝑥108
(7.39𝑥1014 )
= 4.06𝑥10−7 𝑚
3. A certain red light has a wavelength of 6.8x10 -7 m. What is the frequency of the light?
c
λ
f=
3𝑥108
(6.8𝑥10−7 )
= 4.4𝑥1014 ℎ𝑧
4. What is the energy of a quantum of light from question 3?
E = hf
(6.6x10-34)( 4.4𝑥1014 ℎ𝑧) = 2.9x10-19J
5. A certain blue light has a frequency of 6.91 x 1014 Hz. What is the wavelength of the
light?
λ=
c
f
3𝑥108
(6.91𝑥1014 )
= 4.34𝑥10−7 𝑚
6. What is the energy of a quantum of light from question 5?
E = hf
(6.6x10-34)( 6.91 x 1014) = 4.56x10-19J
7. The energy for a quantum of light is 2.84 x 10-19 J. What is the wavelength of this light?
λ=
𝒉𝒄
𝑬
(6.6𝑥10−34 )( 3𝑥108 )
(2.84 x 10−19 )
= 6.97x10-7m
Energy, Wavelength and Frequency Calculation Notes and Problems
1.) Which has a longer wavelength, orange or violet light? orange
2.) Which has a higher energy, x-rays or gamma rays? gamma
3.) Look at the EM spectrum and equations above to answer this question. As you move across the
visible light spectrum from red to violet, state whether each variable increases or decreases.
(A) wavelength decreases
(B) frequency increases
(C) energy increases
4.) A beam of microwaves has a frequency of 1.0 x 10 9 Hz. A beam of radio waves has a frequency of 5.0
x 106 Hz. No calculation is necessary. Which one…
(A) has a longer wavelength? The one with the lower frequency (radio)
(B) is closer to visible light on the EM spectrum? Microwaves
(C) is closer in energy to x-rays? Microwaves
5.) A photon of light has a wavelength of 3.20 x 105 meters. Find…
(A) the frequency
3𝑥108
c
f=λ
(3.2𝑥105 )
= 937.5hz
(B) the energy E = hf
(6.6x10-34)( 937.5) = 6.18x10-31J
(C) type of radiation
radio waves
6.) A photon of light has energy equal to 4.00 x 10-19 J. Find…
(A) the frequency
𝐸
ℎ
=𝑓
4𝑥10−19
6.6𝑥10−34
c
f
(B) the wavelength
λ=
(C) type of radiation
visible light
= 6.06x1014hz
3𝑥108
(6.06𝑥1014 )
= 4.95x10-7m
7.) An emission spectrum of a specific element contains a line with a wavelength of 5.18 x10 -7m.
Determine…
c
λ
(A) the frequency
𝑓=
(B) the energy
(C) the color
E=hf
Green
3𝑥108
(5.18𝑥10−7 )
= 5.79x1014hz
(6.6x10-34)( 5.79x1014hz) = 3.82x10-19J