The electron in a hydrogen atom makes a transition from a state n _...

The electron in a hydrogen atom makes a transition from a state ${n}_{1}$ to ${n}_{2}$ . If the time period of the electron in the initial state is eight times that in the final state, then the possible values of ${n}_{1}$ and ${n}_{2}$ & are&

Options

A ${n}_{1} = 8, {n}_{2} = 2$
B ${n}_{1} = 4, {n}_{2} = 2$
C ${n}_{1} = 3, {n}_{2} = 1$
D ${n}_{1} = 4, {n}_{2} = 1$

Correct answer

B. ${n}_{1} = 4, {n}_{2} = 2$

Step-by-step solution

In a hydrogen atom, the time period obeys the following relation

$T ∝ n^{3}$
$⇒ \dfrac{T1}{T2} = \left(\dfrac{n1}{n2}\right)^{3}$

$⇒ \dfrac{8}{1} = \left(\dfrac{n1}{n2}\right)^{3}$

$⇒ \dfrac{n1}{n2} = \dfrac{2}{1}$

Thus, ${n}_{1} = 4$ and ${n}_{2} = 2$

Practice Atomic Physics on Quantrex Academy →

More from Atomic Physics

Consider a hydrogen atom with v_k , r_k , and K_k denoting the velocity, orbital radius… JEE Advanced 2026 The ratio of momentum of the photons of the 1^ st and 2^ nd line of Balmer series of… JEE Main 2026 In the hydrogen atom, the electron makes a transition from the higher orbit ( i ) to a… JEE Main 2026 In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound… JEE Main 2026 Using Bohr's model, calculate the ratio of the magnetic fields generated due to the… JEE Main 2026 Angular momentum of an electron in a hydrogen atom is (3h)/(π) , then the energy of the… JEE Main 2026 Two electrons are moving in orbits of two hydrogen like atoms with speeds 3 × 10^ 5 ~m /… JEE Main 2026 In hydrogen atom spectrum, (R arrow Rydberg's constant ) A. the maximum wavelength of the… JEE Main 2026 Full Atomic Physics list All NTA Abhyas JEE Main PYQs