Question

1. Calculate the energy (in kJ/mol) of the Lyman series line for hydrogen that is, the transition from n=2 to n=1 (1 kJ/mol= 8.6 cm^-1)

2. Would you expect the energy of the same transition as in the first problem to be greater or less for the helium ion, He^+? Why? Make a sketch to relative scale the energy levels that give rise to the Lyman bands in H-atoms and He^+.

Answer 1

1) We use Rydberg equation

wavenumber of transition = 109737.3 cm-1 ( 1/n1^2 -1/n2^2)   is formula for Hydrogen atom

wavenumber = 109737.3 ( 1/1^2 - 1/2^2) = 82302.975 cm-1e

we have 1KJ/mol = 8.6 cm-1

E in KJ/mol for tranistion = ( 82302.975 /8.6) = 9570 KJ/mol

2) for He^+ atom , Z = 2 ( atomic number)

waveunumver = Z^2 x 109737.3 ( 1/n1^2 -1/n^2)

since Z =2 , Z^2 = 4 , hence we expect higher wavenumbe and thus higher energy.

Orbitals are closer as nuclear charge increases from H to He, hence energy for transition increases as orbitals have higher energy in He^+

E for transitionof He+ = 4 x E for transition for case of H atom