Question

The energy of second Bohr orbit of Hydrogen atom is -328kJmol^-1;hence the energy of fourth Bohr orbit would be?
1)-41 kJ/mol
2)-82kJ/mol
3)-164 kJ/mol
4)-1312 kJ/mol
Pls help me out

Answer 1

We know that Energy of nth orbit of a hydrogen atom is -2.18 × 10⁻¹⁸J ×(1/n²), where n is the respective orbit

⇒ From above expression we can say that Energy of a orbit of hydrogen atom is inversely proportional to n²

⇒ Eᵃ/Eᵇ = (nᵇ)²/(nᵃ)²

Given the Energy of 2nd orbit = -328 kJ/mol

⇒ Eᵃ = E₂ = -328 and nᵃ = 2

We need to find the Energy of 4th orbit

⇒ nᵇ = 4 and Eᵇ = E₄

Substituting the above values in the equation we get :

⇒ -328/E₄ = 4²/2²

⇒ E₄ = -328/4 = -82 kJ/mol

So the Energy of 4th orbit is -82 kJ/mol