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

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