Question

If the speed of an electron of hydrogen atom in the ground state is 2.2 x 10⁶ m/s, then its speed in the third excited state will be ______.

Options

• 5.5 x 10⁶ m/s

• 5.5 x 10⁵ m/s

• 8.8 x 10⁵ m/s

• 6.8 x 10⁶ m/s

Answer 1

If the speed of an electron of hydrogen atom in the ground state is 2.2 x 10⁶ m/s, then its speed in the third excited state will be 5.5 x 10⁵ m/s.

Explanation:

Speed of electron of hydrogen atom In ground state,

v₁ = 2.2 x 10⁶ m/s

Since, `"v" prop 1/"n"`

`therefore "v"_1/"v"_2 = "n"_2/"n"_1 = (2.2 xx 10^6)/"v"_2`     [for third excited state, n₂ = 4]

`=> "v"_2 = (2.2 xx 10^6)/4 = 0.55 xx 10^6` m/s

= 5.5 × 10⁵ m/s