Answer to Question #132854 in Physical Chemistry for Taekyung

Question

Calculate the wavelength, λ, in meters of a photon capable of exciting an electron in He+ from the ground state to n = 4.

Answer 1

Ans.

The energy of an electron in n^th orbit of He⁺ ion = E_n​= −13.6eV×Z²/n².

Here Z = 2 for He

The energy required for transition from n = 1 to n =4 is = -13.6x4 x (1/16 - 1) = 51ev = 8.16 x 10^-8 J

The energy of a photon E = hc/λ where h =plank constant, c = velocity of light in vacuum, λ = wavelength of photon

Now E = 8.16 x 10^-8 J, h = 6.626 x 10^-27 JS, c = 3 x 10⁸ m/s

Putting these values, λ = 2.436 x 10^-11 m (Ans.)