Question

If in Bohr’s model, the time period of revolution is represented as $T_{n,z}$ (where $n$ represents shell number and $Z$ represents atomic number). Then the value of $T_{1,2}:T_{2,1}$ will be:

• A. 8 : 1
• B. 1 : 8
• C. 1 : 1
• D. 1 : 32

Answer 1

The correct option is D 1 : 32

Time period of revolution in nth Bohr's orbit is given by, $T_n=\frac{2\pi r_n}{v_n}$
According to Bohr's model of atom, $r_n\propto \frac{n^2}{Z}$ and $v_n\propto \frac{Z}{n}$
Therefore, $T_n\propto \frac{\left(\frac{n^2}{Z}\right)}{\left(\frac{Z}{n}\right)}$ or $T_n\propto \frac{n^3}{Z^2}$
Applying it for the given question, we get
$T_{1,2}:T_{2,1}=\frac{\left(\frac{1^3}{2^2}\right)}{\frac{2^3}{1^2}}=1:32$