# Problem: Calculate the energy of a photon of wavelength 0.154 nm .

###### FREE Expert Solution

We're asked to calculate the energy of a photon of wavelength 0.154 nm.

Recall that the energy of a photon is given by:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{h\nu }}}$

E = energy = J
▪h = Planck's constant = 6.626x10-34 J
s
▪ν = frequency = Hz or s-1

In the equation, the frequency of the photon is used but the wavelength is given. We can relate frequency and wavelength using the speed of light:

The relationship between wavelength and frequency is as follows:

$\overline{){\mathbf{\lambda }}{\mathbf{=}}\frac{\mathbf{c}}{\mathbf{\nu }}}$

c = speed of light = 3.0x108 m/s
▪ λ = wavelength, m

Rearranging the above equation

$\overline{)\mathbf{c}\mathbf{=}\mathbf{\lambda }\mathbf{·}\mathbf{\nu }}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{c}}{\mathbf{\lambda }}\mathbf{=}\frac{\overline{)\mathbf{\lambda }}\mathbf{·}\mathbf{\nu }}{\overline{)\mathbf{\lambda }}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{\nu }}{\mathbf{=}}\frac{\mathbf{c}}{\mathbf{\lambda }}}$

###### Problem Details

Calculate the energy of a photon of wavelength 0.154 nm .