In Bohr's theory of hydrogen atom, 'r' is the radius of the orbit, 'V' is the speed of electron and E is the total energy of the electron. Out of the following which physical quantity is inversely proportional to principal quantum number?

Step-by-step solution

According to Bohr's theory of hydrogen atom: Radius of the n -th orbit, r n^2 Speed of the electron in the n -th orbit, V 1 n Now, evaluating the given options: For Vr , we have Vr ( 1 n )(n^2) Vr n For 1 Vr , we have 1 Vr 1 n For V^2r , we have V^2r ( 1 n^2 )(n^2) V^2r n^0 For Vr^2 , we have Vr^2 ( 1 n )(n^4) Vr^2 n^3 Thus, the quantity 1 Vr is inversely proportional to the principal quantum number n . Answer: 1 Vr