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The radius of the second orbit in an atom of hydrogen is R. What is the radius of the third orbit?
Asked in GSEB Board July 2017; GSEB Board March 2018 · Postulates, radius, speed and angular momentum
- (1) 3R
- (2) 2.25R
- (3) 9R
- (4) R/3
Answer: (2) 2.25R
Step-by-step solution
Given: r₂=R.
Idea: in the Bohr model rₙ∝ n² for a given atom.
(r₃)/(r₂)=(3²)/(2²)=9/4.
r₃=9/4R=2.25R.
Why the other options are wrong
- (1) No single slip gives 3R. Sanity check: r∝ n², so going from n=2 to n=3 multiplies the radius by 9/4=2.25, not by 3.
- (3) 9R treats R as the radius of the first orbit and multiplies by 3². Here R belongs to the second orbit, so the factor is (3²)/(2²).
- (4) R/3 makes the outer orbit smaller than the inner one, but Bohr orbits get larger as n increases.
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