Question

Using the Bohr's model calculate the speed of the electron in a hydrogen atom in the $\pi=1,2$ and 3 levels.

• A. $4.2 \times 10^{4} m / s , 3.2 \times 10^{4} m / s$ and $7.2 \times 10^{6} m / s$
• B. $2 \times 10^{9} m / s , 3.2 \times 10^{5} m / s$ and $7 \times 10^{5} m / s$
• C. $2.19 \times 10^{6} m / s , 1.01 \times 10^{6} m / s$ and $7.3 \times 10^{5} m / s$
• D. $2.2 \times 10^{6} m / s , 1.9 \times 10^{6} m / s$ and $7.5 \times 10^{4} m / s$

Answer 1

Answer: (C)

Speed of the electron in Bohr's $n$ th orbit $v=\frac{ C }{n} \alpha$
where, $\alpha=\frac{2 \pi K e^{2}}{c h}$
$\alpha=0.0073$
$\therefore v=\frac{C}{n} \times 0.0073$
For $n=1, \, v_{1}=\frac{C}{1} \times 0.0073$
$=3 \times 10^{8} \times 0.0073$
$=2.19 \times 10^{6} m / s$
For $n=2,\, v_{2}=\frac{c}{2} \times 0.0073$
$=\frac{3 \times 10^{8} \times 0.0073}{2}$
$=1.095 \times 10^{6} m / s$
For $n=3,\, v_{3}=\frac{c}{3} \times 0.0073$
$=\frac{3 \times 10^{8} \times 0.0073}{3}$
$=7.3 \times 10^{5} m / s$