In Bohr’s model of the hydrogen atom, what is the ratio of the radius of the 5th orbit to that of the 8th orbit?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 25 : 64
The Bohr model gives the radius of the nth orbit of the hydrogen atom as
\( \displaystyle r_n=\frac{n^2}{m}\left(\frac{h}{2\pi}\right)^2\frac{4\pi\varepsilon_0}{e^2} \)
Everything except \( n \) is a constant, so the radius is proportional to the square of n.
\( \begin{aligned} \frac{r_5}{r_8} &= \frac{5^2}{8^2} \\ &= \frac{25}{64} \end{aligned} \)
Hence, \( r_5:r_8 \) is 25 : 64.