## Chem – Calculating the Energy of Light

What sections should I know before attempting to learn this section?

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?

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?

Step 3:

What is the formula the question involves?

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:

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?

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?

Step 3:

What is the first formula the question involves?

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:

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?

If the energy of a light wave is 2.9 * 10-9 J, what is the frequency?

If the wavelength of a light wave is 1.4 * 10-8 m, what is the energy?  