Consider a hydrogen atom with vₖ, rₖ, and Kₖ denoting the velocity, orbital radius and kinetic energy of the electron in the kth orbit, respectively. The electron undergoes a transition from the nth orbit, emitting radiation corresponding to the Lyman series. Considering h to be Planck’s constant and ε₀ the permittivity of free space, the correct statement(s) is/are:
Select all that apply

Question

Consider a hydrogen atom with vₖ, rₖ, and Kₖ denoting the velocity, orbital radius and kinetic energy of the electron in the kth orbit, respectively. The electron undergoes a transition from the nth orbit, emitting radiation corresponding to the Lyman series. Considering h to be Planck’s constant and ε₀ the permittivity of free space, the correct statement(s) is/are:

Select all that apply

G1 Physics · Accepted Answer

In the Bohr model, mvr = nh/(2π), K = e²/(8πε₀r), and total energy E = −K. Using v/r together with mvr = nh/(2π) gives the stated kinetic-energy change in option A. The emitted frequency is |ΔE|/h = [e²/(8πε₀h)](1/r₁ − 1/rₙ), so C is correct. The other two expressions do not have the correct dependence.