NTA Abhyas JEE Main2020PhysicsNuclear PhysicsPractice
A radioactive sample contains 2.2 mg of pure C 6 11 which has a half-life period of 1224 seconds. Calculate the number of atoms present initially, and the activity when 5 μg of the sample will be left.
Options
- A2.1 × 10 20   atoms,     3.3 × 10 14   dps
- B3.1 × 10 19   atoms,     2.6 × 10 13   dps
- C2.3 × 10 19     atoms,     1.6 × 10 13   dps
- D1.2 × 10 20 atoms, 1.55 × 10 14 dps
Correct answer
D. 1.2 × 10 20 atoms, 1.55 × 10 14 dps
Step-by-step solution
Number of atoms present initially = 6.023 × 10 23 × 2.2 × 10 − 3 11 = 1.2 × 10 20 atoms No. of atoms present in 5 μg of the sample N = 6.023 × 10 23 × 5 × 10 − 6 11 = 2.74 × 10 17 atoms Activity of the sample = λ N = 0.693 T 1 2 × N = 0.693 × 2.74 × 10 17 1224 = 1.55 × 10 14 disintegrations/second