Question

The velocity of an electron in a certain Bohr's orbit of H-atom bears the ratio 1:550 to the velocity of light. The quantum number n of the orbit is:

• A. n = 2
• B. n = 5
• C. n = 3
• D. n = 4

Answer 1

The correct option is D n = 4

Given that:
$\text{Velocity of electron}=\frac{1}{550}\times \text{velocity of light}$
But we know velocity of electron in Bohr orbit is:
$V_n=\frac{2.19\times {10}^8\times Z}{n}cm/sec\therefore \frac{2.19\times {10}^8\times 1}{n}=\frac{1}{550}\times 3\times {10}^{10}\therefore n=\frac{2.19\times {10}^8\times 550}{3\times {10}^{10}}=4$
Hence answer is 4.