Question

Determine the energy of the electron in the 1s orbital of a helium ion (He+ )

Answer 1

He Rydberg formula can be extended for use with any hydrogen-like chemical elements. 
1/ λ = R*Z^2 [ 1/n1^2 - 1/n2^2] 
where 
λ is the wavelength of the light emitted in vacuum; 
R is the Rydberg constant for this element; R 1.09737x 10^7 m-1 
Z is the atomic number, for He, Z =2; 
n1 and n2 are integers such that n1 < n2 
The energy of a He+ 1s orbital is the opposite to the energy needed to ionize the electron that is 
taking it from n = 1 (1/n1^2 =1) to n2 = ∞ (1/n2^2 = 0) 
.: 1/ λ = R*Z^2 = 1.09737x 10^7*(2)^2 
λ = 2.278*10^-8 m 
E = h*c/λ 
Planck constant h = 6.626x10^-34 J s 
c = speed of light = 2.998 x 10^8 m s-1 
E = (6.626x10^-34*2.998 x 10^8)/(2.278*10^-8) = 8.72*10^-18 J ion-1 
Can convert this value to kJ mol-1: 
(8.72*10^-18*6.022 x 10^23)/1*10^3 = 5251 kJ mol-1 
Lit value: RP’s secret book: 5240.4 kJ mol-1 (difference is due to a small change in R going from H to He+) 
So energy of the 1s e- in He+ = -5251 kJ mol-1