(i) The energy associated with the first orbit in the hydrogen atom is –2.18 × 10^–18 J atom^–1. What is the energy associated with the fifth orbit?

(ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.

(i) Energy of an electrons = - (2.18× 10^-18)/n²

Where n = principal quantum number

Now the Energy associated with the fifth orbit of hydrogen atom is

E₅ = -(2.18× 10^-18)/(5)² = -2.18× 10^-18/25

E₅ = -8.72 × 10^-20J

(ii) Radius of Bohr’s n^th for hydrogen atom is given by,

R_n = (0.0529nm) / n2

For,

N = 5

R₅ = (0.0529 nm) (5)²

R₅ = 1.3225 nm