## Question 1:

A photon with an energy of 1.33 x 10^{-21} Joules has a frequency of?

### Answer

The **answer to this question is 2.01 x 10 ^{12} Hz**

Here is how I solved it:

**Data**

The first thing you will need to do is to extract your data from the above question. Here is the vital information we identified:

The energy of the photon, E = 1.33 x 10^{-21} Joules [ The unit of Energy of a photon is in Joules (J)]

Planck’s constant, h = Constant = 6.63 x 10^{-34} Joules-Second [ The unit of Planck’s constant is Joules-Second (J.s)]

**The quantity to find:**

Frequency, f = ?

**The formula to apply:**

The formula to calculate the frequency of the photon is E = hf

**Solution**

From our formula, we have E = hf

But we are looking for the frequency, f

Hence, we make the f subject of the formula from the expression E = hf.

The first step is to divide both sides by h to obtain

f = E/h

We can then go ahead to substitute our values from our data into the above expression

f = 1.33 x 10^{-21} J / 6.63 x 10^{-34} J.s

You can see that for the units above, Joules (J) will cancel Joules (J) to leave us with per second (1/S or s^{-1} which is also the unit of frequency)

Therefore, we can write it as

f = (1.33 x 10^{-21} J / 6.63 x 10^{-34}) s^{-1} [ we can change s^{-1} to Hz if we want to do so]

Now, apply a calculator to solve 1.33 x 10^{-21} J ÷ 6.63 x 10^{-34}

Therefore, we will now get

f = 2,006,033,182,503.77 = 2.01 x 10^{12} s^{-1} or 2.01 x 10^{12} Hz.

**Therefore, the photon with an energy of 1.33 x 10 ^{-21} Joules has a frequency of 2.01 x 10^{12} Hz**

## Question 2:

A photon with an energy of 1.33 x 10^{-21} Joules has a wavelength of?

### Answer

The **answer to this question is 1.5 x 10^{-5} meters**.

Here is the proof:

**Data:** Identify your data from the question

The energy of the photon, E = 1.33 x 10^{-21} Joules [ The unit of Energy of a photon is in Joules (J)]

Planck’s constant, h = Constant = 6.63 x 10^{-34} Joules-Second [ The unit of Planck’s constant is Joules-Second (J.s)]

Speed of light, c = 3.0 x 10^{8} m/s

**The quantity to find:**

The wavelength, λ =?

**The formula to apply:**

E = hc/λ

Here is how I arrived at the formula:

The formula to calculate the energy of a photon is E = hf, and frequency, f = c/λ

Hence, E = h x c/λ = hc/λ

**Solution**

Since E = hc/λ

We can make the λ subject of the formula from the above expression

After cross-multiplication

The formula for calculating wavelength, λ = hc/E [**Note:** The unit of wavelength of a photon is in meters (m)]

Now, insert your values from the data you obtained from the question into the above expression to get

Wavelength, λ = (6.63 x 10^{-34} x 3.0 x 10^{8})/1.33 x 10^{-21}

The above expression is now equal to

λ = (6.63 x 10^{-34} x 3.0 x 10^{8})/1.33 x 10^{-21}

Therefore, we will now get

λ = 1.989 x 10^{-25}/1.33 x 10^{-21} = 0.00015 m or 1.5 x 10^{-5} m

**Therefore, the photon with an energy of 1.33 x 10 ^{-21} Joules has a wavelength of 1.5 x 10^{-5} meters**.

**You can also calculate the energy of a photon by applying the** energy of a photon calculator.

*You may also like to read:*

How to Calculate the Work Function of a Metal

Solved Problem: How to Calculate the Wavelength of Radiation

How to Calculate the Kinetic Energy of an Ejected Electron

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Calculate the Energy of a Photon of Each Frequency