Question

The angular momentum of an electron in a given stationary state can be expressed as $m_{e}vr=n\frac{h}{2\pi }$. Based on this expression an electron can move only in those orbits for which its angular momentum is ?

• A. Equal to n
• B. Integral multiple of $\frac{h}{2\pi }$
• C. Multiple of n
• D. Equal to $\frac{h}{2\pi }$ only.

Answer 1

The correct option is B Integral multiple of $\frac{h}{2\pi }$

According to Bohr's postulates:

The angular momentum of an electron in a given stationary state can be expressed as:

$m_{e}vr=n\frac{h}{2\pi }$

where $m_e$=mass of electron, $v$=velocity of electron, $r$=radius of Bohr orbit, $n=n^{th}$ Bohr orbit (Integral value)

Thus an electron can move only in those orbits for which its angular momentum is an integral multiple of $\frac{h}{2\pi }$ that is why only certain fixed orbits are allowed.

This explains the stability of an atom by giving a condition for an allowed orbit.