Q88 / 90 · JEE Main 2023 (15 Apr Shift 1) · Physics

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths $(i . e . \frac{λ_{1}}{λ_{2}})$ is $\frac{7}{4 n}$ , then the value of $n$ will be

Correct answer: 5

Solution

For $λ_{1}$
$\frac{1}{λ_{1}} = R Z^{2} (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = R (\frac{5}{36}) . . . (i)$
For $λ_{2}$ ,
$\frac{1}{λ_{2}} = R Z^{2} (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = R (\frac{7}{144}) . . . (i i)$
Dividing (ii) by (i)
$\frac{λ_{1}}{λ_{2}} = \frac{\frac{7}{144}}{\frac{5}{36}} = \frac{7}{20}$
So,
$\frac{7}{4 n} = \frac{7}{20} \Rightarrow n = 5$

Hence, the correct answer is 5.

Relevant Questions

In hydrogen atom spectrum, Rydberg's constant A. the maximum wavelength of the radiation of Lyman series is B. the Balmer series lies in the23 Jan, 2026 (M)Atomic Spectrum
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly nm .22 Jan, 2026 (E)Atomic Spectrum
For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is.07 Apr, 2025 (M)Atomic Spectrum
The number of spectral lines emitted by atomic hydrogen that is in the energy level, is29 Jan, 2025 (E)Atomic Spectrum
During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is and it becomes when the ele24 Jan, 2025 (M)Atomic Spectrum
Arrange the following in the ascending order of wavelength : (A) Microwaves (B) Ultraviolet rays (C) Infrared rays (D) X-rays Choose the mos24 Jan, 2025 (E)Atomic Spectrum

As per given figure A, B and C are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengthsi.e. λ1λ2 is 74n, then the value of n will be

Solution

Relevant Questions

As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths $(i . e . \frac{λ_{1}}{λ_{2}})$ is $\frac{7}{4 n}$ , then the value of $n$ will be