## Guide:

Here is a comprehensive guide on how to calculate the threshold frequency of quantum energy:

- To calculate threshold frequency, we need to read and understand the question.

2. Read the question for the first time.

3. Try reading the question again, but this time underline any numerical figures.

4. Think of the formula that best fits the question

5. The formula for the frequency (f) of quantum energy is f = c/ λ [where c=speed of light in vacuum, and λ=wavelength of the radiation]

6. Relate the variables from the formula with what you have underlined

7. Update your data

8. Solve the problem

10. Another formula we can apply to calculate threshold frequency involves the question that mentioned the work function of a metal which is f_{0} = w_{0}/h [ where f_{0} = threshold frequency, w_{0} = work function of a metal, and h= Planck’s constant = 6.6×10^{-34}Js

## Examples of How to Calculate the Threshold Frequency of Quantum Energy

Here are a few examples to guide you.

### Example 1

Calculate the frequency of quantum of quantum energy carried by radiation of wavelength 3 x 10^{-6}m, where c is the speed of electromagnetic waves which is about 3 x 10^{8}m/s.

**Solution**

**Data:**

Wavelength of the radiation, λ = 3 x 10^{-6}m

Speed of light in vacuum, c = 3 x 10^{8}m/s

Frequency, f = ?

since f = c/ λ

We can substitute our data into the above formula for frequency

f = 3 x 10^{8}/3 x 10^{-6} = 10^{14}Hz

Therefore, the frequency of quantum of energy is 10^{14}Hz

### Example 2

The work function of metal sodium is 20ev. If Planck’s constant is 6.6×10^{-34}Js, calculate the threshold frequency of the metal.

**Solution**

**Data:**

The work function, w_{0} = 20ev = 3.2×10^{-19}J

speed of light in vacuum, c = 3×10^{8}m/s

Planck’s constant, h=6.6×10^{-34}Js

f_{0} = ?

We substitute our formula f_{0} = w_{0}/h to get

f_{0} = 3.2×10^{-19}/6.6×10^{-34} = 4.8×10^{14}

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**Reference**