CUET · PHYSICS · PYQ PAPER 2025

The smallest wavelength in the spectral lines of Paschen series in the hydrogen atom is (Given: \( R = 1.097 \times 10^{7} \text{ m}^{-1} \))

A 4102 \( \text{\AA} \)
B 6304 \( \text{\AA} \)
C 8204 \( \text{\AA} \)
D 9846 \( \text{\AA} \)

Verified Solution

Answer & Solution

Correct Answer

(C) 8204 \( \text{\AA} \)

Step-by-step Solution

Detailed explanation

\( \frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \) \( n_f = 3 \), \( n_i = \infty \) \( \lambda = \frac{9}{R} \) \( \lambda = \frac{9}{1.097 \times 10^{7} \text{ m}^{-1}} \) \( \lambda = 8.204 \times 10^{-7} \text{ m} = 8204 \text{ \AA} \)

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

A potential difference of 6 V is applied across a conductor of length 12 cm. If the mobility of electrons is \( 5.6 \times 10^{-6} \text{ m}^2/\text{V}\cdot\text{s} \), their drift velocity will be:

CUET 2025 Easy

List I contains physical quantities related to mechanical oscillations of a block of mass m attached to spring of force constant k. List II contains physical quantities related to a LC oscillator. Match List I with List II.

List I	List II
(A) Mass m	(I) Charge q
(B) Force Constant k	(II) Inductance L
(C) Displacement x	(III) Reciprocal capacitance 1/C
(D) Velocity ( \(v=\frac{d x}{d t}\) )	(IV) Current \(\left(i=\frac{d q}{d t}\right)\)

On the basis of analogies between mechanical and electrical quantities;
Choose the correct answer from the options given below:

CUET 2023 Hard

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