Atomic Physics Question 5
Question 5 - 30 January - Shift 1
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 :
(1) $(1.8 \times 10^{6})$
(2) $(7.5 \times 10^{6})$
(3) $(3.6 \times 10^{6})$
(4) $(8.4 \times 10^{6})$
Show Answer
Answer: (4)
Solution:
Formula: Radius And Speed Of Electron In Hydrogen Like Atoms
$ V_n \propto \frac{Z}{n} $
$Z=1, \therefore V_n \propto \frac{1}{n}$
$\therefore \frac{V_3}{V_7}=\frac{7}{3}$
$\therefore V_3=\frac{7}{3} V_7$
$ \begin{aligned} & =\frac{7}{3} \times 3.6 \times 10^{6} m / s \\ & =8.4 \times 10^{6} m / s \end{aligned} $
