Question

In an Hydrogen like atom, the electron moves around the nucleus in circular orbits of radius $R$. It is excited to the orbit of radius $4R$. The ratio of the time taken by the electron to complete one revolution in the orbit of radius $R$ to that of orbit of radius $4R$ is:

• A. $1:2$
• B. $1:4$
• C. $8:1$
• D. $1:8$

Answer 1

The correct option is D $1:8$

$r_n=K{n}^2$ Since Z is same for same element
We know that radius of a Bohr orbit of a Hydrogen like atom is proportional to $n^2$
Thus we can conclude R corresponds to n = x and 4R corresponds to n =2x
Similarly For the same element time period
$T_n\propto n^3$
$\therefore \frac{T_x}{T_{2x}}=\frac{1}{8}$