CUET · PHYSICS · PYQ PAPER 2023

The half life of a radioactive substance is 30 s. Calculate the time taken for the sample to decay to \( \frac{3}{4} \) th its initial value.

A 30 s
B 20 s
C 40 s
D 60 s

Verified Solution

Answer & Solution

Correct Answer

(D) 60 s

Step-by-step Solution

Detailed explanation

\( \frac{N}{N_0} = 1 - \frac{3}{4} = \frac{1}{4} \) \( \frac{N}{N_0} = \left(\frac{1}{2}\right)^{t/T_{1/2}} \) \( \frac{1}{4} = \left(\frac{1}{2}\right)^{t/30} \) \( \left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)^{t/30} \) \( 2 = \frac{t}{30} \) \( t = 60 \text{ s} \)

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

Explore more questions on app

From CUET

Match List - I with List - II.

List - I	List - II
(A) \(\left(y^{\prime \prime}\right)^3+\sin \left(y^{\prime}\right)=e^x\)	(I) 2
(B) \(\left(y^{\prime \prime}\right)^2+\left(y^{\prime}\right)^3=\sin x\)	(II) 1
(C) \(y^{\prime \prime \prime}+5 y^{\prime \prime}+6 y^{\prime}+3 y=\cos x\)	(III) Not defined
	(IV) 3

Choose the correct answer from the options given below :

CUET 2023 Easy

Explore more questions on app