Question

If m is mass of electron, v its velocity, r the radius of stationary circular orbit around a nucleus with charge Ze, then from Bohr's second postulate, the kinetic energy `"K.E." = 1/2"mv"^2` of the electron in C.G.S. system is 2 equal to ____________.

Options

• `1/2 "Ze"^2/"r"`

• `1/2 "Ze"^2/"r"^2`

• `"Ze"^2/"r"`

• `"Ze"/"r"^2`

Answer 1

If m is mass of electron, v its velocity, r the radius of stationary circular orbit around a nucleus with charge Ze, then from Bohr's second postulate, the kinetic energy `"K.E." = 1/2"mv"^2` of the electron in C.G.S. system is 2 equal to `1/2 "Ze"^2/"r"`.

Explanation:

In the revolution of electron, coulomb force provides the necessary centripetal force

`therefore "Ze"^2/"r"^2 = "mv"^2/"r"`

`therefore "mv"^2 = "Ze"^2/"r"`

`therefore "K.E" = 1/2"mv"^2 = "Ze"^2/(2"r")`