CBSE Class 12 · 2020 · Modern PhysicsShort Answer

Define the term 'half-life' of a radioactive substance. Two different radioactive substances have half-lives

T_{1}

and

T_{2}

and the number of undecayed atoms at an instant are

N_{1}

and

N_{2}

respectively. Find the ratio of their activities at that instant.

Answer: $R_{1} / R_{2} = N_{1} T_{2} / (N_{2} T_{1})$ .

Solution

Half-life

T_{1/2}

: the time in which the number of undecayed nuclei of a sample reduces to half its initial value.
Activity

R = λ N = \frac{0.693}{T _{1/2}} N

. Therefore

\frac{R _{1}}{R _{2}} = \frac{λ _{1} N _{1}}{λ _{2} N _{2}} = \frac{N _{1} / T _{1}}{N _{2} / T _{2}} = \frac{N _{1} T _{2}}{N _{2} T _{1}} .

\frac{R _{1}}{R _{2}} = \frac{N _{1} T _{2}}{N _{2} T _{1}}

CBSE Class 12 Board · 2020 · Subjective