Scientific Understanding

**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} m^{2}kg/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 * 10^{21} Hz, how much energy does one this wave contain?

**Step 1:**

What information are we given?

Answer:

frequency = f = 7.5 * 10^{21} Hz

Plank’s constant = h = 6.626 * 10^{-34} m^{2}kg/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} m^{2}kg/s (7.5 * 10^{21} 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 * 10^{4} m, how much energy does one of these waves contain?

**Step 1:**

What information are we given?

Answer:

wavelength = λ = 2.8 * 10^{4} m

speed of light = c = 3.0 * 10^{8} 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} m^{2}kg/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 * 10^{4} m(f) = 3.0 * 10^{8} m/s

**Step ****5****:**

How do we rearrange the equation to solve for frequency (f)?

Answer: Divide both sides by 2.8 * 10^{4} m

2.8 * 10^{4} m(f) = |
3.0 * 10^{8} m/s |

2.8 * 10^{4} m |
2.8 * 10^{4} m |

**Step ****6****:**

Cross out like terms

2.8 * 10^{4} m(f) = |
3.0 * 10^{8} m/s |

2.8 * 10^{4} m |
2.8 * 10^{4} m |

**Step ****7****:**

Simplify

f = | 3.0 * 10^{8} m/s |

2.8 * 10^{4} m |

**Step ****8****:**

What is the answer for the frequency (f)?

f = 10714 Hz or about 1.07 * 10^{4} 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} m^{2}kg/s (1.07 * 10^{4} 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 * 10^{8} m/s and Plank’s constant = h = 6.626 * 10^{-34} m^{2}kg/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 * 10^{24} 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