Question

The velocity of an electron in a certain Bohr's orbit of $H{e}^{+}$ ion bears the ratio 1:550 to the velocity of light. The quantum number n of the orbit is:

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

The correct option is C 8

Given that:
$\text{Velocity of electron}=\frac{1}{550}\times \text{velocity of light}$
But we know velocity of electron in Bohr orbit is:
$V_n=\frac{2.19\times {10}^8\times Z}{n}cm/sec\therefore \frac{2.19\times {10}^8\times 2}{n}=\frac{1}{550}\times 3\times {10}^{10}\therefore n=\frac{2.19\times {10}^8\times 550\times 2}{3\times {10}^{10}}\approx 8$
Hence the answer is 8.