The masses of two radioactive substances are same and their half-lives are 1 year and 2 years, respectively. The ratio of their activities after 6 years will be

Step-by-step solution

Let initial masses of two radioactive substances be N₀ . If T₁ and T₂ be the half-lives of two radioactive substances, Then, T₁=1 yr Hence, remaining mass of the first substances after aligned t &=6 yrs N₁ &=N₀ ( 1 2 )^ t T =N₀ ( 1 2 )^ 6 / 1 &= N₀ 2⁶ N₁ &= N₀ 64 aligned Similarly, remaining mass of the second substance after t=6 y r ~s N₂=N₀ ( 1 2 )^ t T₂ =N₀ ( 1 2 )^ 6 / 2 = N₀ 8 N₂= N₀ 8 N₁ N₂ = N₀ 64 N₀ 8 = 1 8 N₁ N₂ = 1 8 Since, activity, A= N= 0.693 T N A N T A₁ A₂ = N₁ T₂ N₂ T₁ = 1 8 2 1 = 1 4 A₁: A₂=1: 4