Answer:
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.
