It takes 245 kj/mol to eject electrons from a certain metal surface. what is the longest wavelength of light (nm) that can be used to eject electrons from the surface of this metal via the photoelectric effect?

longest wavelength is 489 nm

Explanation:

The energy per mol required to eject electrons from this  metal is given. We can calculate what is the energy required for one electron ( this value is known as the work function for the metal ), and from there make use of the equation: E = hc/λ to calculate the  wavelength, λ .

E = (245 x 10 ³ J / mol ) / 6.022 x 10²³ atom/mol = 4.1 x 10⁻¹⁹ J

E = h c/ λ   ⇒  λ = h c/ E

where h: Planck´s constant, 6.63 x 10⁻³⁴ Js

           c: speed of ligth, 3 x 10⁸ m/s

Therefore,

λ = 6.63 x 10⁻³⁴ Js x 3 x 10⁸ m/s/  4.1 x 10⁻¹⁹ J = 4.89 x 10⁻⁷ m

To convert to nm  multiply by the conversion factor, 1 x 10⁹ nm = 1 m

4.89 x 10⁻⁷ m  x 1 x 10⁹ nm /m = 489 nm

Therefore the maximum wavelength is 489 nm. Any light with a wavelength greater than this value will not have enough energy to eject electrons from this metal.

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