Question

The radioactivity of a sample is R₁ at a time T₁ and R₂ at a time T₂. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T₁ – T₂) is proportional to(a) (R₁T₁ – R₂T₂)(b) (R₁ – R₂)(c) (R₁ – R₂)/T(d) (R₁ – R₂) T

Answer 1

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Option B is Correct

Answer 2

Answer:

D) (R1 - R2) T

Explanation:

Radioactivity of sample = R1 and R2 (Given)

Time of sample = T1 and T2 (Given)

Radioactivity of sample at time T1 is represented as - R1 = λ N1

Radioactivity of sample at time T2 is  represented as - R2 = λ N2

Number of atoms that have disintegrated in the time (T2-T1) = N1 -N2

= (R1 - R2 /λ)

λ = 0.693/T

Therefore,

(T2-T1)  = (R1 - R2) T/ 0.693

(T2-T1)  α (R1 - R2)T

Thus, the number of atoms that have disintegrated in the time (T₁ – T₂) is proportional to (R1 - R2)T