Question

The binding energy of electrons to a chromium metal surface is 7.21 × 10-19 J. What is the longest wavelength of light (in nm) that will eject electrons from chromiummetal? What frequency is required to give electrons with kinetic energy of 5.09E-19 J? What wavelength (in nm) is required to give electrons with kinetic energy of5.09E-19 J?

Answer 1

1. Binding energy = photon energy = hc/λ

where h is Planck constant, c is speed of light and λ is wavelength

7.21 x 10^-19 = 6.626 x 10^-34 x 2.998 x 10⁸/λ

Wavelength λ = 2.76 x 10^-7 m = 276 nm

2. Photon energy = binding energy + kinetic energy

= 7.21 x 10^-19 + 5.09 x 10^-19

= 1.23 x 10^-18 J = hf

where f is frequency

Frequency f = 1.23 x 10^-18/6.626 x 10^-34

= 1.856 x 10¹⁵ ≈ 1.86 x 10¹⁵ Hz

3. Wavelength λ = c/f

= 2.998 x 10⁸/1.856 x 10¹⁵

= 1.62 x 10^-7 m = 162 nm