Question

If the speed of the electron in the first Bohr orbit of hydrogen atom be $x$ then the speed of the electron in the third Bohr orbit is-

• A. $\frac{x}{9}$
• B. $\frac{x}{3}$
• C. $x$
• D. $9x$

Answer 1

The correct option is B $\frac{x}{3}$

The speed of electron in $n^{th}$ Bohr’s orbit for hydrogen atom is given by,

$v_n=\frac{2\pi K{e}^{2}Z}{nh}=2.188\times {10}^6\left(\frac{Z}{n}\right){\text{ms}}^{-1}$

For the first Bohr orbit of $H-$ atom,

$Z=1,n=1$

$v_1=2.188\times {10}^6{\text{ms}}^{-1}=x$

Now the speed of electron in third Bohr orbit is,

$v_3=\frac{2.188\times {10}^6}{3}{\text{ms}}^{-1}=\frac{x}{3}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.