Answer to Question #17913 in Physical Chemistry for Aidan242

Question

Calculate the wavelength, in metres, of a photon capable of exciting an electron in He+ from the ground state to n=4... Someone please tell me the right answer urgently :( ?

Answer 1

Energy levels for the hydrogen-like He⁺ are given by
E(n) = -Z²*R/n², where Z = 2;

Energy of an absorbed photon between the levels n=1 and m=4
E(m,n) = Z²*R*(1/n² - 1/m²)

We will take R = 10973731.6 m^-1, Rydberg constant for H, in reciprocal meters.

Photon wavelength
lambda = h*c/E = 1/Z²*R*(1/n² - 1/m²)) = 1/(2²*10,973,731.6 m^-1*(1/1² - 1/4²)) = 3.746*10^-8 m

Answer: 3.746*10^-8 meters