Question

Using Bohr's model, the orbital period of electron in hydrogen atom in nth orbit is (ε₀ = permittivity of free space, h = Planck's constant, m = mass of electron and e = electronic charge)

Options

• `(2ε_0^2"n"^3"h"^3)/"me"^4`

• `(8ε_0^2"n"^3"h"^3)/"me"^4`

• `(2ε_0"n"^2"h"^2)/"me"^4`

• `(4ε_0^2"n"^3"h"^3)/"me"^4`

Answer 1

`(4ε_0^2"n"^3"h"^3)/"me"^4`

Explanation:

The orbital period of revolution of electron in nth orbit is

`"T"_"n" = (2pi"r"_"n")/"v"_"n"`

As, we know, `"r"_"n" = (("h"^2ε_0)/(pi"me"^2)) "n"^2/"Z"`

and `"v"_"n" = ("e"^2/(2"h"ε_0))"Z"/"n"`

∴ `"T"_"n" = 2pi ("h"^2ε_0"n"^2)/(pi"me"^2"Z") xx (2"h"ε_0"n")/("e"^2"Z")`

`= (4ε_0^2 "n"^3"h"^3)/("me"^4"Z"^2)`

For hydrogen atom, Z = 1

∴ `"T"_"n" = (4ε_0^2 "n"^3"h"^3)/("me"^4)`