Question

Let R1 be the radius of the second stationary orbit and R2 be the radius of the fourth stationary orbit of an electron in Bohr's model, The ratio \[\frac{R_1}{R_2}\] is:

Options

• 0.25

• 0.5

• 2

• 4

Answer 1

0.25

Explanation:

As,

\[R_n=0.529\frac{n^2}{Z}\]

Hence,

\[\frac{R_1}{R_2}=\frac{0.529\frac{n_1^2}{Z_1}}{0.529\frac{n_2^2}{Z_2}}\]

\[\frac{R_1}{R_2}=\frac{n_1^2}{n_2^2}=\frac{(2)^2}{(4)^2}\]

∴ \[\frac{R_1}{R_2}=\frac{1}{4}=0.25\]