Question

If the velocity of the electron in first orbit of hydrogen atom is $2.18\times {10}^6\text{m/s}$, what is its value in third orbit?

• A. $7.27\times {10}^6\text{m/s}$
• B. $7.27\times {10}^5\text{m/s}$
• C. $6.54\times {10}^6\text{m/s}$
• D. $6.54\times {10}^5\text{m/s}$

Answer 1

The correct option is B $7.27\times {10}^5\text{m/s}$

The velocity of electron in a Bohr orbit is proportional to $\frac{Z}{n}$
For H- atom, Z = 1
$\therefore \frac{v_1}{v_3}=\frac{n_3}{n_1}=\frac{3}{1}$
Velocity of electron in $3^{rd}$ Bohr orbit of $H-atom=\frac{2.18\times {10}^{6}m/s}{3}=7.27\times {10}^{5}m/s$