Question

How do you calculate the energy of a photon with an electromagnetic wave of wavelength 420 nm?

Answer 1

There is a relation between energy and frequency. The formula which shows the relation between energy, frequency and wavelength is as follows.

$$\Rightarrow v=\dfrac{c}{\lambda } \\\ \Rightarrow E=h\dfrac{c}{\lambda } \\\$$

Where E = energy of the photon
H = Planck’s constant
c = velocity of the wave
$\lambda$ = wavelength of the wave

Complete step-by-step answer: - In the question it is asked to calculate the energy of the photon which has a wavelength of 420 nm.
- The question contains the data that the wavelength of the electromagnetic radiation is 420 nm.
- Means $\lambda$ = 420 nm.
- The formula used to calculate the energy of the photon is as follows.

$$E=hv \\\ \Rightarrow v=\dfrac{c}{\lambda } \\\ \Rightarrow E=h\dfrac{c}{\lambda } \\\$$

Where E = energy of the photon
H = Planck’s constant = $6.6023\times {{10}^{23}}$
c = velocity of the wave = $3\times {{10}^{8}}$
$\lambda$ = wavelength of the wave = 420 nm
- Substitute all the values in the above formula to get the energy of the photon.

$$E=h\dfrac{c}{\lambda } \\\ \Rightarrow E=6.023\times {{10}^{23}}\times \dfrac{3\times {{10}^{8}}}{420} \\\ \Rightarrow E=4.73\times {{10}^{-19}}or2.95ev. \\\$$

- The energy of the electromagnetic radiation with a wavelength of 420 nm is $4.73\times {{10}^{-19}}$ J or 2.95 ev (electron volt) .
- The energy and the frequency of the electromagnetic radiation are directly proportional to the frequency of the electromagnetic radiation.

Note: The energy of the photon is inversely proportional to the wavelength of the photon. The energy of the photon can be expressed in joules or electron volt (ev). Energy of the electromagnetic radiation is going to change with wavelength of the electromagnetic radiation.