Question

Silver has a work function, Φ, of 4.64 eV. If a sample of silver is bombarded with 215 nm photons, what will be the wavelength (in meters) of the photo-ejected electrons? (1 eV = 1.60 × 10⁻¹⁹ J, the mass of an electron is 9.109 x 10⁻³¹ kg, and Planck's constant is 6.626 x 10⁻³⁴ Js.)​

Answer 1

Given info : Silver has a work function, Φ, of 4.64 eV. If a sample of silver is bombarded with 215 nm photons.

To find : the wavelength of the photoejected electrons is..

solution : we know, E = hν + Φ

incident energy, E = hν =  hc/λ

h = 6.626 × 10⁻³⁴ Js

c = 3 × 10⁸ m/s

= 215 nm = 2.15 × 10⁻⁷ m

= (6.626 × 10⁻³⁴×  3 × 10⁸)/(2.15 × 10⁻⁷)

= (6.626 × 3)/(2.15) × 10⁻¹⁹

= 9.245 × 10⁻¹⁹ J

now, work function, Φ = 4.64 eV = 4.64 × 1.6 × 10⁻¹⁹ C = 7.424 × 10⁻¹⁹ J

∴ 9.245 × 10⁻¹⁹ = hν +  7.424 × 10⁻¹⁹

⇒ (9.245 - 7.424)  × 10⁻¹⁹ = hc/λ₁

⇒ 1.821 × 10⁻¹⁹ = (6.626 × 10⁻³⁴ × 3 × 10⁸)/λ₁

⇒ λ₁ = (6.626 × 3)/1.821 × 10⁻⁷ m = 10.916 × 10⁻⁷ m = 1091.6 nm

therefore the wavelength of the photoejected electrons is 1091.6 nm (approx).