Question

Find the energy of a photon with a wavelength of 820. nm?

Answer 1

Answer: The energy of a photon with a wavelength of 820 nm is
`2.42 * 10^(-19) m`.

Step-by-step explanation:

Given : Wavelength = 820 nm

Convert nm into meter as follows.

`1 nm = 10^(-9)\\So, 820 nm = 820 nm * (10^(-9) nm)/(1 nm)\\= 820 * 10^(-9) m`

The relation between energy and wavelength is as follows.

`E = (hc)/(\lambda)`

where,

E = energy

h = Planck's constant =
`6.63 * 10^(-34) kg m^(2)/s`

c = speed of light =
`3.0 * 10^(8) m/s`

`\lambda` = wavelength

Substitute the values into above formula as follows.

`E = (hc)/(\lambda)\\= (6.63 * 10^(-34) kg m^(2)/s * 3.0 * 10^(8) m/s)/(820 * 10^(-9) m)\\= (1.989 * 10^(-25))/(820 * 10^(-9))\\= 2.42 * 10^(-19) m`

Thus, we can conclude that energy of a photon with a wavelength of 820 nm is
`2.42 * 10^(-19) m`.