# Problem: The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kJ/mol . What wavelength (in nm) of light has sufficient energy per photon to dislodge an electron from the surface of sodium?

###### FREE Expert Solution

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

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

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

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

Substitute in the energy equation:

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###### Problem Details

The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kJ/mol . What wavelength (in nm) of light has sufficient energy per photon to dislodge an electron from the surface of sodium?