Question

A photon has a wavelength of 705nm calculate the energy of the photon in joules

Answer 1

Answer: The energy of the photon is
`2.82* 10^(-19)J`

Step-by-step explanation:

The relation between energy and wavelength of light is given by Planck's equation, which is:

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

where,

E = energy of the photon

h = Planck's constant =
`6.626* 10^(-34)Js`

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

`\lambda` = wavelength of photon = 705 nm =
`705* 10^(-9)m` (Conversion factor:
`1m=10^9nm` )

Putting values in above equation, we get:

`E=(6.626* 10^(-34)Js* 3.0* 10^8m/s)/(705* 10^(-9)m)\\\\E=2.82* 10^(-19)J`

Hence, the energy of the photon is
`2.82* 10^(-19)J`

Answer 2

In calculating the energy with a given wavelength, just use the Planck’s Equation. First calculate for the frequency using the wave equation. Just divide the speed of light which is 3x10^8 m/s with the given wavelength (705x10^-9 m). Then multiply the frequency with the Planck constant which is 6.63 x10^-34 J. The answer would be 2.82x10^-19 J.