Question

If J be the angular momentum of an electron in an Bohr orbit then orbit radius is equal to :
1. \(\frac{J}{mv}\)
2. \(\frac{J}{2mv}\)
3. \(\frac{J}{2 \pi m}\)
4. \(\frac{mJ}{2\pi v}\)

Answer 1

Correct Answer - Option 1 : \(\frac{J}{mv}\)

Ans: Option: 1

CONCEPT: 

• Angular Momentum: The moment of momentum is called angular momentum.

  • It is the property of any rotating object given by moment of inertia times angular velocity.

• Bohr's postulate 2: In a hydrogen atom, the electron can revolve around the nucleus, without radiating energy, only in those orbits for which the angular momentum of the electron is equal to an integral multiple \(\frac{h}{2\pi }\) of where h is Planck's constant.

Angular momentum (J) = m v r = \(\frac{nh}{2\pi }\)

Where m is the mass of the electron, v is the velocity of the electron and r is the radius of the orbit

EXPLANATION:

Angular momentum (J) = m v r = \(\frac{nh}{2\pi }\)

by solving we get,  \(r= \frac{J}{mv}\)