CUET · PHYSICS · PYQ PAPER 2023

What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen atom spectrum lines ?
(Take \( h = 6.63 \times 10^{-34} \text{ Js} \); \( c = 3 \times 10^8 \text{ ms}^{-1} \); \( e = 1.6 \times 10^{-19} \text{ C} \))

A \( 122 \text{ nm} \)
B \( 12.2 \text{ nm} \)
C \( 1.22 \text{ nm} \)
D \( 10.2 \text{ nm} \)

Verified Solution

Answer & Solution

Correct Answer

(A) \( 122 \text{ nm} \)

Step-by-step Solution

Detailed explanation

For least energetic photon in Lyman series: \( n_f = 1, n_i = 2 \). \( \frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) = 1.097 \times 10^7 \text{ m}^{-1} \left( \frac{1}{1^2} - \frac{1}{2^2} \right) \)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List - I with List - II.

List - I (Electromagnetic waves)	List - II (Uses)
(A) Radio waves	(I) Aircraft navigation
(B) Ultraviolet rays	(II) Physical therapy
(C) Infrared waves	(III) Television communication systems
(D) Microwaves	(IV) Kill germs in water purifiers

Choose the correct answer from the options given below :

CUET 2023 Medium

Explore more questions on app

From CUET

Explore more questions on app

What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen atom spectrum lines ?(Take \( h = 6.63 \times 10^{-34} \text{ Js} \); \( c = 3 \times 10^8 \text{ ms}^{-1} \); \( e = 1.6 \times 10^{-19} \text{ C} \))

Step-by-step Solution

What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen atom spectrum lines ?
(Take \( h = 6.63 \times 10^{-34} \text{ Js} \); \( c = 3 \times 10^8 \text{ ms}^{-1} \); \( e = 1.6 \times 10^{-19} \text{ C} \))