The time taken for a radioactive sample to decay to 1/16th of its initial activity is: MCQ with Answer and Explanation

The time taken for a radioactive sample to decay to 1/16th of its initial activity is:
A. 4 half-lives
B. 8 half-lives
C. 2 half-lives
D. 3 half-lives
Answer: Option A
Solution (By JKSSB Mock Tests)
After n half-lives, activity reduces to (1/2)ⁿ of initial. Set (1/2)ⁿ = 1/16 ⇒ (1/2)ⁿ = (1/2)⁴ ⇒ n = 4 half-lives. Thus time = 4 × half-life. Memory aid: '1/2ⁿ remaining after n half-lives; 1/16 = 1/2⁴ ⇒ 4 half-lives'. This radioactivity calculation is frequently tested in competitive exams. Always express fraction as power of 1/2 to find half-life count. This problem assesses understanding of exponential decay without heavy computation.

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Practice More Physics Questions

Question #1
Assertion (A): A fuse wire must have a high resistance and a low melting point. Reason (R): This ensures it melts quickly and breaks the circuit when an excessively high current flows.
A. Both A and R are true but R is NOT the correct explanation of A.
B. A is true but R is false.
C. Both A and R are true and R is the correct explanation of A.
D. A is false but R is true.

Correct Answer: Option C


Explanation:
A fuse is a safety device. It must have a relatively high resistance so that it produces heat quickly when a large current passes through (H = I²Rt). It must have a low melting point so that this heat causes it to melt immediately, breaking the circuit and protecting appliances. Thus, both A and R are true, and R explains A.

This question belongs to: Science Physics
Question #2
Heat required to convert 1 g of ice at 0°C to water at 0°C is (latent heat 80 cal/g)
A. 100 cal
B. 80 cal
C. 1 cal
D. 540 cal

Correct Answer: Option B


Explanation:
Latent heat of fusion of ice = 80 cal/g. So 1 g needs 80 cal. No temperature change.

This question belongs to: Science Physics
Question #3
The angle of minimum deviation for a prism depends on:
A. Refractive index only
B. Angle of prism only
C. Wavelength of light only
D. Both angle of prism and refractive index

Correct Answer: Option D


Explanation:
Minimum deviation δ_m for a prism: n = sin[(A + δ_m)/2] / sin(A/2), where A is prism angle, n refractive index. Thus δ_m depends on both A and n. Since n varies with wavelength (dispersion), δ_m also depends on wavelength, but the primary dependencies are A and n. Memory tip: 'δ_m increases with A and n; used to measure n'. This optics formula application is frequently tested in competitive exams. Always recall that minimum deviation occurs when ray passes symmetrically through prism, a key condition for derivation.

This question belongs to: Science Physics