Question

If the velocity of electron in first orbit of H-atom is $2.18\times {10}^{6}m/sec$ then the velocity of an electron in 4th orbit of ${He}^{+}$ ion is: ( Given c is velocity of light in m/sec)

• A. $\frac{c}{275}$
• B. $\frac{c}{312}$
• C. $\frac{c}{137}$
• D. $\frac{c}{217}$

Answer 1

The correct option is A $\frac{c}{275}$

Since, it is given that the velocity of the electron in first orbit of H atom $=2.18\times {10}^{6}m/s,$ Z= 2, n= 4

So, $v_3=(2.18\times {10}^6)\frac{Z}{n}=(2.18\times {10}^6)\frac{2}{4}=\frac{3\times {10}^8}{137\times 2}=\frac{c}{274}$ or $\frac{c}{275}$