Question

number of revolutions per second made by electron in bohr orbit is called orbital frequency. which represents the orbital if un,rn,En are velocity,radius and energy level of nth orbit respectively

Answer 1

Since we are considering a hydrogen atom, we can apply Bohr’s model. We know,

v=v0n2r=r0n2

where v and r denote the orbital velocity and radius of orbit of the electron, and v0 and r0 are (known) constants.

Clearly, the angular velocity of the electron is
ω=vr∝1n3

The frequency of revolution is
ν=ω2π∝1n3

Thus,
νnν2=4⟹(2n)3=4⟹n=2–√3≈1.26

But obviously, the principal quantum number cannot be a non-integer. So, we infer that the situation stated in the problem infact cannot occur. The problem has the solution 1 if instead of 4, the orbital frequency is 8 times that of the second orbit.