A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will ____

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

Q. A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

(A) increase by 64 times

(B) decrease by 4 times

(D) increase by 8 times

Correct Answer: decrease by 4 times

Explanation

Let the initial radius of the spherical detector be R.

Volume of a sphere is proportional to the cube of its radius:

V ∝ R³

Given that the volume increases by 8 times:

V₂ = 8V₁

So,

R₂³ = 8R₁³

R₂ = 2R₁

Intensity of radiation from a point source follows the inverse square law:

I ∝ 1 / R²

Therefore,

I₂ / I₁ = (R₁ / R₂)²

I₂ / I₁ = (1 / 2)²

I₂ / I₁ = 1 / 4

Hence, the intensity becomes one-fourth of its original value.

So, the intensity decreases by 4 times.