The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

Solution

Physics sir · 3 steps

Bohr radius grows as n², so going from orbit 3 to orbit 4 multiplies it by 16/9.

1. Radius rule. In Bohr's model the radius of the nth orbit is rₙ = n²/Z × 0.529 Å. For the same atom Z is fixed, so rₙ ∝ n².

   r₄/r₃ = 4²/3² = 16/9

2. Put in R. The third orbit has r₃ = R, so r₄ = 16/9R. This is larger than R, as it should be, because higher orbits lie farther from the nucleus.
3. So. The radius of the fourth orbit is 16/9R, which is option (b).

The idea to keep. For Bohr orbits of one atom, radius goes as n², speed as 1/n and energy as 1/n². Take the ratio and square the orbit numbers for radius.

Answer from the NTA final answer key. Solution by PrepWiser.