Question

In a hypothetical system a particle of mass m and charge -3q is moving around a very heavy particle having charge q. Assuming Bohr's model to be true to this system, The orbital velocity of mass m when it is nearest to heavy particle is

• A. $\frac{3q^2}{2{\epsilon }_{0}h}$
• B. $\frac{4q^2}{2{\epsilon }_{0}h}$
• C. $\frac{3q}{2{\epsilon }_{0}h}$
• D. $\frac{3q}{4{\epsilon }_{0}h}$

Answer 1

The correct option is A $\frac{3q^2}{2{\epsilon }_{0}h}$

$\begin{array}{c}\text{Given,}\\ \text{a hypothetical system}\\ \text{Bohr's model is true by}\\ \text{assuming.}\end{array}$

$\begin{array}{cc}I)F_{\text{centripetal}}& =\text{culoumb force}\\ & \frac{m{v}^2}{r}=\frac{1\times q\times +3q}{4\pi {\epsilon }_0\times r^2}\\ & mvr=\frac{3q^2}{4\pi {\epsilon }_{0}v}\cdots \left(1\right)\end{array}$

$\begin{array}{c}\text{II) Angular momentum}=\frac{nh}{2\pi }\\ mvr=\frac{nh}{2\pi }\text{(ii)}n=\text{no of orbit}\\ h=\text{plank constant}\end{array}$

$\begin{array}{c}\left(i\right)=\left(ii\right)\\ \frac{nh}{2\pi }=\frac{3q^2}{4\pi {\epsilon }_{0}v}\end{array}$

$\begin{array}{c}\text{for}n=1\\ \begin{array}{c}\frac{h}{2\pi }=\frac{3q^2}{4\pi {\epsilon }_{0}v}\\ \text{velocity in}{1}^{\text{st}}\text{orbit}\left(v\right)=\frac{3q^2}{2{\epsilon }_{0}h}\end{array}\end{array}$