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, $\alpha =\frac{2\pi K{e}^2}{ch}$
$\alpha =0.0073$
$\therefore v=\frac{C}{n}\times 0.0073$
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 $n=3,v_3=\frac{c}{3}\times 0.0073$
$=\frac{3\times 10^8\times 0.0073}{3}$
$=7.3\times 10^{5}m/s$