Question

Calculate the energy required to ionize a ground state hydrogen atom. report your answer in kilojoules.

Answer 1

First we find for the wavelength of the photon released due to change in energy level. We use the Rydberg equation:

1/ʎ = R [1/n1^2 – 1/n2^2]

where,

ʎ is the wavelength

R is the rydbergs constant = 1.097×10^7 m^-1

n1 is the 1st energy level = 1

n2 is the higher energy level = infinity, so 1/n2 = 0

 

Calculating for ʎ:

1/ʎ = 1.097×10^7 m^-1 * [1/1^2 – 0]

ʎ = 9.1158 x 10^-8 m

 

Then calculate the energy using Plancks equation:

E = hc/ʎ

where,

h is plancks constant = 6.626×10^−34 J s

c is speed of light = 3x10^8 m/s

 

E = (6.626×10^−34 J s * 3x10^8 m/s) / 9.1158 x 10^-8 m

E = 2.18 x 10^-18 J = 2.18 x 10^-21 kJ

 

This is still per atom, so multiply by Avogadros number = 6.022 x 10^23 atoms / mol:

E = (2.18 x 10^-21 kJ / atom) * (6.022 x 10^23 atoms / mol)

E = 1312 kJ/mol