Question

Dimensional formula for activity of a radioactive substance is

• A. $[M^{0}L^{1}T^{-1}]$
• B. $[M^{0}L^{-1}T^{0}]$
• C. $[M^{0}L^{0}T^{-1}]$
• D. $[M^{-1}L^{0}T^{0}]$

Answer 1

The Correct Option is C

Activity \( A \) of a radioactive substance is defined as the number of disintegrations per unit time. The unit of activity is the Becquerel (Bq), which is equal to 1 disintegration per second (1 Bq = 1 disintegration/second). The dimensional formula for the number of disintegrations is dimensionless because it counts the number of disintegrations. The time dimension is involved because activity is a rate.

Thus, the dimensional formula for activity is: \[ [A] = T^{-1} \] This implies that the dimensional formula for the activity of a radioactive substance is: \[ M^0 L^0 T^{-1} \] Therefore, the correct answer is (C) \( M^0 L^0 T^{-1} \).

Answer 2

The activity of a radioactive substance is defined as the rate at which the nuclei of the substance undergo decay. The SI unit of activity is the Becquerel (Bq), which is equal to 1 decay per second. Thus, the activity \( A \) of a substance is related to the number of disintegrations per unit time. The dimension of time \( T \) in the activity formula is \( T^{-1} \), and since activity is a count of events per second, it has no dependence on mass or length. Therefore, the dimensional formula of activity is: \[ A \propto \frac{1}{T} \quad \text{or} \quad [A] = M^0 L^0 T^{-1} \] Thus, the correct dimensional formula for activity is \( M^0 L^0 T^{-1} \).