Question

The radius of the fourth orbit of hydrogen is $0.85nm$. Calculate the velocity of an electron in this orbit $(m_e=9.1\times {10}^{-31}kg)$.

• A. $4.3\times {10}^6$ $m$ ${sec}^{-1}$.
• B. $5.44\times {10}^5$ $m$ ${sec}^{-1}$.
• C. $9.24\times {10}^5$ $m$ ${sec}^{-1}$.
• D. $7\times {10}^6$ $m$ ${sec}^{-1}$.

Answer 1

Answer: (B)

$5.44\times {10}^5$ $m$ ${sec}^{-1}$.

$\because mvr=\frac{nh}{2\pi }$

For $4^{th}$ orbit, $mvr=\frac{4h}{2\pi }$

$\therefore V=\frac{2h}{mr\pi }=\frac{2\times 6.626\times {10}^{-23}}{9.1\times {10}^{-31}\times 0.85\times {10}^{-19}\times 3.14}m/s=5.44\times {10}^5$ $m/s$