Question

The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light (c) is ____________.

(h = Planck's constant, ε₀ = permittivity of free space, e = charge on electron)

Options

• `(2"e"^2ε_0)/("hc")`

• `"e"^3/(2ε_0"hc")`

• `"e"^2/(2ε_0"hc")`

• `(2ε_0"hc")/"e"^2`

Answer 1

The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light (c) is `underline("e"^2/(2ε_0"hc"))`.

Explanation:

The speed of an electron in the hydrogen atom's n^th state is

v_n = `("e"^2/(2"h"ε_0)) 1/"n" "m"//"s"`

For ground state (n = 1) v₁ = `"e"^2/(2"h"ε_0)` m/s

∴ `"v"_1/"c" = "e"^2/(2ε_0"hc")`