Question

3. Two radioactive substances A and B initially
contain equal number of nuclei. A has half life of
1 hour and B has a half life of 3 hour. After 6 hour,
the ratio of activity of A to that of B is
Answer is 1)3/16. How?​

Answer 1

Answer:

Two radioactive substances A and B initially contain equal number of nuclei.

Half life of A = 1hr

Half life of B = 3hr

We have to find the ratio of their activity after 6hr.

▪ Radioactive sample of A :

» No of half live = 6/1 = 6

» Radioactive sample of A left after 6 hrs (N) = (1/2)$^6$ × No

▪ Radioactive sample of B :

» No of half lives = 6/3 = 2

» Radioactive sample of B left after 6 hrs (N')= (1/2)² × No

↗ No denotes initial number of nuclei.

✴ Decay constant of A :

▪ (Φ)A = ln2/T(1/2) = ln2/1 = ln2

✴ Decay constant of B :

▪ (Φ)B = ln2/T(1/2) = ln2/3

↗ T(1/2) denotes half life.

❇ Activity of A after 6 hrs :

▪ R = (Φ)A × N

▪ R = ln2 × (1/2)$^6$ × No

❇ Activity of B after 6 hrs :

▪ R' = (Φ)B × N'

▪ R' = ln2/3 × (1/2)² × No

☣ Ratio of Activity :

→ R/R' = 3 × 1/2$^4$

→ R/R' = 3/16

→ R : R' = 3 : 16