Question

In the Bohr model of the hydrogen atom, let R, V and E represent the radius of the orbit, speed of the electron and total energy of the electron respectively. Which of the following quantity is proportional to the quantum number n ?

• (A) $E/V$
• (B) $R/E$
• (C) $VR$
• (D) $RE$

Answer 1

The Correct Option is C

Explanation:
Given:Radius of the orbit is RVelocity of the electron is VTotal energy of the electron is EVelocity of an electron in the n^th orbit of Bohr's model of an atom is given byV $\alpha \frac{1}{n}$...... (i)The radius of the orbit is given byR $\alpha n^2$...... (ii)The energy of an electron in the nth orbit is given byE $\alpha n^2$........ (iii)A. For option (A)E/V = $\frac{n}{n^2}=\frac{1}{n}$Option 'A' is incorrect.B. For option (B)R/E = n⁴Option 'B' is incorrect. C. For option (C)V.R = $\frac{n^2}{n}=n$Option 'C' is correct.D. For option (D)R.E = $\frac{n^2}{n^2}=1$Option 'D' is incorrect.Hence, the correct option is (C).