Question

The energy of second Bohr orbit of the hydrogen atom is
-328 kJ mol⁻¹; hence the energy of fourth Bohr orbit would
be:
(a) -41 kJ mol⁻¹ (b) -82 kJ mol⁻¹
(c) -164 kJ mol⁻¹ (d) -1312 kJ mol⁻¹

Answer 1

The energy of fourth Bohr orbit would  be:

(b) -82 kJ mol⁻¹

We know that energy of an electron for Hydrogen atom in the Bohr's orbit is given as -13.6/n² eV

= (-13.6*96)/n² kJ mol⁻¹            [1 eV ≈96 kJ mol⁻¹]

For the fourth orbit, n = 4

Putting the value of n as 4 in the above expression, we get

E = (-13.6*96)/4² kJ mol⁻¹  

= (-13.6*96)/16 kJ mol⁻¹  

= -81.6 kJ mol⁻¹

≈ 82  kJ mol⁻¹

So, option (b) is correct.