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# a photon with an energy of 1.33

## Question 1:

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

The answer to this question is 2.01 x 1012 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 1012 s-1 or 2.01 x 1012 Hz.

Therefore, the photon with an energy of 1.33 x 10-21 Joules has a frequency of 2.01 x 1012 Hz

## Question 2:

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

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 108 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 108)/1.33 x 10-21

The above expression is now equal to

λ = (6.63 x 10-34 x 3.0 x 108)/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.

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