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Physics Question on Bohr's model of hydrogen atom

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

(A) E/V

B

(B) R/E

C

(C) VR

D

(D) RE

Answer

(C) VR

Explanation

Solution

Explanation:
Given:Radius of the orbit is RVelocity of the electron is VTotal energy of the electron is EVelocity of an electron in the nth orbit of Bohr's model of an atom is given byV α1n...... (i)The radius of the orbit is given byR α n2...... (ii)The energy of an electron in the nth orbit is given byE α n2........ (iii)A. For option (A)E/V = nn2=1nOption 'A' is incorrect.B. For option (B)R/E = n4Option 'B' is incorrect. C. For option (C)V.R = n2n=nOption 'C' is correct.D. For option (D)R.E = n2n2=1Option 'D' is incorrect.Hence, the correct option is (C).