Scientific Tutor
Chem – Calculating the Energy of Light
Author: Andrew
What sections should I know before attempting to learn this section?
—> Calculating the Wavelength and Frequency of Light
How do you calculate the energy of light?
We can also link the frequency calculations to the energy of a wave of light. When the frequency of a wave is HIGH the energy is LARGE. If the frequency is LOW the energy is SMALL. This relationship is also in the equation below.
Energy = Plank’s constant * (frequency)
E = h (f)
In the equation E represents energy and has the units of Joules (J), f stands for frequency and has the units of Hz, and h represents what they call Plank’s constant. Plank’s constant is 6.626 *10-34 m2kg/s.
Notice you can link together the equation for the energy of a wave and the equation for the speed of a wave because they both contain frequency.
VIDEO Energy of Light Calculation Demonstrated Example 1: If the frequency of light is 7.5 * 1021 Hz, how much energy does one this wave contain?
Step 1:
What information are we given?
Answer:
frequency = f = 7.5 * 1021 Hz
Plank’s constant = h = 6.626 * 10-34 m2kg/s (this is a constant that you should always have even if it does not state it in the problem)
Step 2:
What is the problem asking for?
Answer: Energy = E
Step 3:
What is the formula the question involves?
Answer: E = h (f)
Step 4:
How do we fill in the numbers for the formula?
Answer: E = 6.626 * 10-34 m2kg/s (7.5 * 1021 Hz)
Step 5:
COMPLETE ANSWER: about 5.0 * 10-12 J
VIDEO Energy of Light Calculation Demonstrated Example 2: If the wavelength of light is 2.8 * 104 m, how much energy does one of these waves contain?
Step 1:
What information are we given?
Answer:
wavelength = λ = 2.8 * 104 m
speed of light = c = 3.0 * 108 m/s (this is a constant that you should always have even if it does not state it in the problem)
Plank’s constant = h = 6.626 * 10-34 m2kg/s (this is a constant that you should always have even if it does not state it in the problem)
Step 2:
What is the problem asking for?
Answer: Energy = E
Step 3:
What is the first formula the question involves?
Answer: λ (f) = c
Step 4:
How do we fill in the numbers for the formula?
Answer: 2.8 * 104 m(f) = 3.0 * 108 m/s
Step 5:
How do we rearrange the equation to solve for frequency (f)?
Answer: Divide both sides by 2.8 * 104 m
| 2.8 * 104 m(f) = | 3.0 * 108 m/s |
| 2.8 * 104 m | 2.8 * 104 m |
Step 6:
Cross out like terms
| 2.8 * 104 m(f) = | 3.0 * 108 m/s |
| 2.8 * 104 m | 2.8 * 104 m |
Step 7:
Simplify
| f = | 3.0 * 108 m/s |
| 2.8 * 104 m |
Step 8:
What is the answer for the frequency (f)?
f = 10714 Hz or about 1.07 * 104 Hz
Step 9:
What is the second formula the question involves?
E = h (f)
Step 10:
How do we fill in the numbers for the formula?
E = 6.626 * 10-34 m2kg/s (1.07 * 104 Hz)
Step 11:
COMPLETE ANSWER: about 7.1 * 10-30 J
PRACTICE PROBLEMS: Solve for the unknown wavelength, frequency, or energy. Don’t forget you that you have your constants of speed of light = c = 3.0 * 108 m/s and Plank’s constant = h = 6.626 * 10-34 m2kg/s.
If the frequency of light is 3.5 * 106 Hz then what is the energy of the wave?
Answer: 2.3 * 10-27 J
If the energy of a light wave is 2.9 * 10-9 J, what is the frequency?
Answer: 4.4 * 1024 Hz
If the wavelength of a light wave is 1.4 * 10-8 m, what is the energy?
Answer: 1.4 * 10-17 J
If the energy of light is 8.7 * 10-11 J, what is the wavelength of the light?
Answer: 2.3 * 10-15 m
Posted in Chemistry
