Question

The half life of thorium is 3.64 days .After how many days will 0.1 of the mass of sample of the substance remains undecayed?​

Answer 1

12.093 days will take to remain 0.1 of mass of sample of the substance.

It has given that the half life of thorium is 3.64 days.

half life of radioactive decay, T = ln2/λ

⇒3.64 = ln2/λ

⇒λ = ln2/3.64 = 0.1904 day¯¹ ..........(1)

using radioactive decay concept,

t = 1/λ ln{[intia amountl]/[final amount]}

[initial amount] = N, [final amount] = 0.1 N

t = 1/0.1904 ln[N/0.1N]

= 1/0.1904 ln(10)

= 12.093 days

therefore, 12.093 days will take to remain 0.1 of mass of sample of the substance.