Question

The electron of mass 'm' is rotating in first Bohr orbit of radius 'r' in hydrogen atom. The orbital acceleration of the electron in first orbit is ______.

(b =Planck's constant)

Options

• `h^2/(4pi^2m^2r^3)`

• `h/(2pi^2m^2r^2)`

• `h/(4pi^2mr^3)`

• `h^2/(2pi^2m^2r^2)`

Answer 1

The electron of mass 'm' is rotating in first Bohr orbit of radius 'r' in hydrogen atom. The orbital acceleration of the electron in first orbit is `underline(h^2/(4pi^2m^2r^3))`.

Explanation:

The centripetal acceleration is given by

`a="v"^2/r`

By Bohr's second postulate mvr = `h/(2pi)`

Squaring, `m^2"v"^2r^2=h^2/(4pi^2)`

`therefore"v"^2=h^2/(4pi^2m^2r^2)`

`therefore"v"^2/r=h^2/(4pi^2m^2r^3)`