The work function of an element is the energy required to remove an electron from the surface of the solid. The work function for palladium is 503.7 kJ/mol (that is, it takes 503.7 kJ of energy to remove 1 mole of electrons from 1 mole of Pd atoms on the surface of Pd metal). What is the maximum wavelength of light that can remove an electron from an atom in palladium metal

λ = 2.38 × 10^(-7) m

Explanation:

We are given the work function for palladium as 503.7 kJ/mol.

Now let's convert this to KJ/electron.

We know from avogadro's number that;

1 mole of electron = 6.022 × 10^(23) electrons

Thus,

503.7 kJ/mol = 503.7 × 1/(6.022 × 10^(23)) = 8.364 × 10^(-22) KJ/electron = 8.364 × 10^(-19) J/electron

Formula for energy of a photon is;

E = hv

Where;

h is Planck's constant = 6.626 × 10^(-34) J.s

v is velocity

Now, v = c/λ

Where;

c is speed of light = 3 × 10^(8) m/s

λ is wavelength of light.

Thus;

E = hc/λ

Making λ the subject, we have;

λ = hc/E

λ = (6.626 × 10^(-34) × 3 × 10^(8))/(8.364 × 10^(-19))

λ = 2.38 × 10^(-7) m