Question

ΔE= 2.18×10−18 J What is the change in energy, ΔE, in kilojoules per mole of hydrogen atoms for an electron transition from n=3 to n=2?

Answer 1

Answer -

Given,

Initial shell = 3

Final Shell = 2

E in kJ/mol = ?

We know that,

E = -13.6(z²/n²)eV

E₃ = -13.6(1/3²)eV

E₂ = -13.6(1/2²)eV

E = E3-E2

E = -13.6(1/3²)eV - -13.6(1/2²)eV

E = -13.6 [(1/3²)-(1/2²)] eV

E = -13.6 [(1/3²)-(1/2²)] eV

E = 1.88888888889 eV

Also,

1 eV = 1.60218 *10^-22 kJ

So, 1.88888888889 eV = 1.88888888889 * 1.60218 *10^-22 kJ

E = 3.02634 *10^-22 kJ

This change in Energy is for 1 atom. i.e. 3.02634 *10^-22 kJ/atom

Now,

1 mol = 6.023 * 10²³ atom

1 atom = 1mol/6.023 * 10²³

Put this in Energy,

E = 3.02634 *10^-22 kJ/(mol/6.023 * 10²³ )

E = 3.02634 *10^{-22 *} 6.023 * 10²³ kJ/mol

E = 3.02634 *10^{-22 *} 6.023 * 10²³ kJ/mol

E = 182.28 kJ/mol [ANSWER]