Question 35: The radius of inner most orbit of hydrogen atom is 5.3 \times 10^{-11} \mathrm{~m}. What is the radius of third allowed orbit of hydrogen atom?
(1) 1.59 \AA
(2) 4.77 \AA
(3) 0.53 \AA
(4) 1.06 \AA
Answer: Option (2)
Explanation:
According to Bohr’s model of hydrogen atom, the radius of the n^{\text{th}}
orbit is given by r_{n}=n^{2} r_{1}, where r_{1} is the radius of the first orbit.
The radius of the innermost orbit is given as r_{1}=5.3 \times 10^{-11} \mathrm{~m}.
For the third allowed orbit, n=3.
Hence, the radius is r_{3}=3^{2} \times 5.3 \times 10^{-11}.
So, r_{3}=9 \times 5.3 \times 10^{-11}=4.77 \times 10^{-10} \mathrm{~m}.
Since 1 \AA = 10^{-10} \mathrm{~m}, the radius becomes 4.77 \AA.
Hence, the correct answer is Option (2).