The radius of the inner most electron orbit of a hydrogen atom is 0.53 Å. What is the radius of orbit of 2nd excited state?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4.77 Å
In Bohr's model of the hydrogen atom the radius of the \( n \)th orbit is proportional to \( n^{2} \):
\( \displaystyle r_n = n^{2} r_1, \qquad r_1 = 0.53\,\mathring{\mathrm{A}} \)
The ground state is \( n = 1 \), the first excited state is \( n = 2 \), so the second excited state is \( n = 3 \).
\( \displaystyle r_3 = 3^{2} \times 0.53\,\mathring{\mathrm{A}} = 9 \times 0.53\,\mathring{\mathrm{A}} = 4.77\,\mathring{\mathrm{A}} \)