Question

Speed of an electron in Bohr's $7^{\text {th }}$ orbit for Hydrogen atom is $3.6 \times 10^6 m / s$. The corresponding speed of the electron in $3^{\text {rd }}$ orbit, in $m / s$ is :

• A. $\left(3.6 \times 10^6\right)$
• B. $\left(7.5 \times 10^6\right)$
• C. $\left(1.8 \times 10^6\right)$
• D. $\left(8.4 \times 10^6\right)$

Answer 1

Answer: (D)

$V _{ n } \propto \frac{ Z }{ n } $
$ Z =1,$
$\therefore V _{ n } \propto \frac{1}{ n } $
$\therefore \frac{ V _3}{ V _7}=\frac{7}{3} $
$ \therefore V _3=\frac{7}{3} V _7 $
$=\frac{7}{3} \times 3.6 \times 10^6 m / s $
$=8.4 \times 10^6\,m / s $