Question: 33: Let R_{1} be the radius of the second stationary orbit and R_{2} be the radius of the fourth stationary orbit of an electron in Bohr’s model. The ratio \frac{R_{1}}{R_{2}} is :
(1) 0.25
(2) 0.5
(3) 2
(4) 4
Answer: Option (1)
Explanation:
According to Bohr’s model of the hydrogen atom, the radius of the n^{\text{th}} stationary orbit is given by r_{n}=n^{2}a_{0}, where a_{0} is the Bohr radius.
For the second stationary orbit, n=2. Hence, R_{1}=2^{2}a_{0}=4a_{0}.
For the fourth stationary orbit, n=4. Hence, R_{2}=4^{2}a_{0}=16a_{0}.
Now, the required ratio is \frac{R_{1}}{R_{2}}=\frac{4a_{0}}{16a_{0}}=\frac{1}{4}=0.25.
Therefore, the correct option is (1).