In a hydrogen atom, which of the following products do not depend on the principal quantum number n ? The symbols carry their standard meanings.

Step-by-step solution

For a hydrogen atom, the velocity of the electron in the n -th orbit is given by v 1 n . The radius of the n -th orbit is given by r n^2 . The energy of the electron in the n -th orbit is given by E 1 n^2 . Checking the given products: vn 1 n n = 1 , which is independent of n . vr 1 n n^2 = n , which depends on n . En 1 n^2 n = 1 n , which depends on n . Er 1 n^2 n^2 = 1 , which is independent of n . Thus, the products vn and Er do not depend on the principal quantum number n .