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 ______.

विकल्प

• (R₁T₁ - R₂T₂)

• (R₁ - R₂)

• (R₁ - R₂)/T

• (R₁ - R₂) T

Answer 1

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 (R₁ - R₂) T.

Explanation:

Radioactivity at T₁, R₁ = λN₁ 

Radioactivity at T₂, R₂ = λN₂ 

∴ Number of atoms decayed in time

(T₁ - T₂) = (N₁ - N₂)

= `("R"_1-"R"_2)/lambda=(("R"_1-"R"_2)"T")/0.693` ∝ (R₁ - R₂) T