Question

What is the maximum wavelength capable of removing a single electron from the surface of solid rubidium if the work function (binding energy) for rubidium is 208.4 kJ/mol?

Answer 1

Answer :

Step 1: Calculate the energy required to remove one electron from an atom of a solid rubidium

Given,

work function = 208.4 kJ /mol

we know,

1 mol = 6.022 x 10²³ atom

1 kJ = 1000 J

Hence, the energy of a single electron /atom = 208.4 kJ /mol × (1 mol / 6.022 x 10²³ atom) × (1000 J / 1 kJ )

= 3.46 x 10^-19 J/atom

Step 2: Calculation of maximum wavelength

Formula Explanation:

We know

E= hv where h = planck's constant = 6.626 × 10^-34 J-s

frequency (v) = C/λ

and C = 3 × 10⁸ m/s =speed of light

so the equation becomes

or, E= hv

or, E= hc / λ where, E = Energy of one photon

Calculation :

we got,

E_photon = 3.46 x 10^-19 J/atom

hence on substituting the value in above equation we get

λ_max = hc / E_photon

λ = ( 6.626 × 10^-34 J-s × 3 × 10⁸ m/s ) / (3.46 x 10^-19 J/atom) = 5.745 × 10^-7 m = 574.5 nm

hence, the maximum wavelength is 574.5 nm

[ note : 1 m = 10⁹ nm so, 5.745 × 10^-7 m × (10⁹ nm / 1 m ) = 574.5 nm ]