Question

A particle of mass ‘m’ and charge ‘−2q’ is moving around a very heavy particle having charge ‘q’. If Bohr’s model is to be used then the orbital velocity of mass ‘m’ when it is nearest to the heavy particle is (in magnitude) (ε₀ = permittivity of free space, h = Planck’s constant) ______.

Options

• `q^2/(hε_0)`

• `(2q^2)/(hε_0)`

• `q^2/(2hε_0)`

• `(2q^2)/(3hε_0)`

Answer 1

A particle of mass ‘m’ and charge ‘−2q’ is moving around a very heavy particle having charge ‘q’. If Bohr’s model is to be used then the orbital velocity of mass ‘m’ when it is nearest to the heavy particle is (in magnitude) (ε₀ = permittivity of free space, h = Planck’s constant) `bbunderline(q^2/(hε_0))`.

Explanation:

Since the particle of mass ‘m’ is revolving around a heavy particle.

∴ Centripetal force = electrostatic force of attraction

`(mv^2)/r = 1/(4 pi ε_0r) ((q)(-2q))/r^2`

∴ `mv^2 = (-q)^2/(2piε_0r)`

`v = (-q^2)/(2pi ε_0(mvr))`

According to Bohr’s second postulate,

`L = mvr = h/(2 pi)`

∴ `v = (-q^2)/(hε_0)`

∴ `|v| = (q^2)/(hε_0)`