Question

If light with frequency of 2.06×10^3 THz strikes a block of palladium metal, electrons are ejected with a velocity of 1.08×10^6 m/s. Calculate the binding energy of palladium in kJ/mol.

Answer 1

The binding energy of palladium is approximately 399 kJ/mol.

Work function (Φ) = Photon energy (hf) - Electron kinetic energy (1/2 mv²)

Φ =
`(6.63 * 10^-^3^4 Js * 2.06 * 10^1^5 Hz) - (1/2 * 9.11 * 10^-^3^1 kg * (1.08* 10^6 m/s)`²

Φ =
`1.37 * 10^-^1^8 J - 5.89 * 10^-^1^9 \\ = 7.81 * 10^-^1^9 J`

we then Convert work function to electronvolts (eV):

Φ (eV) = Φ (J) / e Φ (eV)

=
`7.81 * 10^-^1^9 J / 1.602 * 10^-^1^9 C`

= 4.87 eV

The ionization energy of palladium is 5.56 eV.

Binding energy (BE) = Φ + IE BE

= 4.87 eV + 5.56 eV BE

= 10.43 eV

BE (kJ/mol) =
`10.43 eV * 6.022 * 10^2^3 * 1 kJ/1000 J * 1 eV/1.602 * 10^-^1^9`

J BE (kJ/mol) = 399 kJ/mol