In a hydrogen atom, which of the following products do not depend...

For a hydrogen atom, the velocity of the electron in the $n$-th orbit is given by $v \propto \dfrac{1}{n}$.

The radius of the $n$-th orbit is given by $r \propto n^2$.

The energy of the electron in the $n$-th orbit is given by $E \propto \dfrac{1}{n^2}$.

Checking the given products:

$vn \propto \dfrac{1}{n} \times n = 1$, which is independent of $n$.

$vr \propto \dfrac{1}{n} \times n^2 = n$, which depends on $n$.

$En \propto \dfrac{1}{n^2} \times n = \dfrac{1}{n}$, which depends on $n$.

$Er \propto \dfrac{1}{n^2} \times n^2 = 1$, which is independent of $n$.

Thus, the products $vn$ and $Er$ do not depend on the principal quantum number $n$.