Question

The radius of orbit of an electron in hydrogen atom in its ground state is 5.3 x 10^-11 m After collision with an electron, it is found to have a radius of 13.25 x 10^-10 m. The principal quantum number n of the final state of the atom is ______.

विकल्प

• n = 4

• n = 5

• n = 16

• n = 3

Answer 1

The radius of orbit of an electron in hydrogen atom in its ground state is 5.3 x 10^-11 m After collision with an electron, it is found to have a radius of 13.25 x 10^-10 m. The principal quantum number n of the final state of the atom is n = 5.

Explanation:

For a hydrogen atom,

`"r"_"n" alpha  "n"^2 => "r"_"1"/"r"_"2" = ("n"_1/"n"_2)^2`

`therefore (5.3 xx 10^-11)/(13.25 xx 10^-10) = "n"_1^2/"n"_2^2`

`therefore "n"_2^2 = 25 => "n"_2 = 5`