Step 1: Check the Units:
The unit of $h/2\pi$ is J s, which is the unit of angular momentum (kg m^2/s). Energy is in joules and radius is in metres, so they cannot be a plain multiple of $h/2\pi$.
Step 2: Recall Bohr's Second Postulate:
Bohr said that the electron moves only in orbits where $m v r = n \dfrac{h}{2\pi}$. This is the quantisation of angular momentum.
Step 3: Look at the Others:
Kinetic energy and potential energy vary as $1/n^2$, and the radius varies as $n^2$. None of them is n times $h/2\pi$.
Step 4: Conclude:
Angular momentum is the quantity that equals $nh/2\pi$, so the answer is option 4.
Final Answer:
\[\boxed{\text{Angular momentum of electron}}\]