Question

In two H-atoms, X and Y, the electrons move around the nucleus in the $1^{st}$ and $2^{nd}$ orbits respectively. The ratio of the time taken by them to complete one revolution is:

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

Answer 1

The correct option is C $1:8$

Time to complete one revolution around the nucleus in the $n^{th}$ Bohr orbit of a H-like atom is given by:
$T_n=1.52\times {10}^{-16}\frac{n^3}{Z^2}s$
For H-atom $Z=1$ i.e. $T_n=1.52\times {10}^{-16}{n}^{3}s$
$\therefore \frac{T_X}{T_Y}=\frac{n_X^3}{n_Y^3}=\frac{1}{8}$