Single Choice

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

AEqual to n
BIntegral multiple of $$\frac{h}{2\pi}$$
Correct Answer
CMultiple of n
DEqual to $$\frac{h}{2\pi}$$ only.

Solution

According to Bohr's postulates:
The angular momentum of an electron in a given stationary state can be expressed as:
$$m_evr=n\frac{h}{2\pi}$$
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.

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