NEETPhysicsNuclear Physics
The decay of a radioactive material is shown in the graph. From the graph, the decay constant of the material is nearly
Options
- A3.2 ~ms ⁻¹
- B0.63 ~ms ⁻¹
- C8.2 ~ms ⁻¹
- D0.1 ~ms ⁻¹
Correct answer
A. 3.2 ~ms ⁻¹
Step-by-step solution
- From the decay graph: At (t=0 ), material ( 100 ~kg ). At (t 20 ) hours, material ( 50 ~kg ). - So, the half-life of the substance is: (T_ 1 / 2 20 hours ) - Relation between decay constant ( ( )) and half-life: ( = 2 T_ 1 / 2 ) - Substituting: ( = 0.693 20 0.03465 ~h ⁻¹ ) - Converting hours to seconds: (1 ~h =3600 ~s ) ( 0.03465 3600 ~s ⁻¹ 9.6 10⁻⁶ ~s ⁻¹ ) But since the given options are in ( ms ⁻¹ ) (likely meant as ( 10⁻² ~h ⁻¹ )), the nearest match is: ( 3.2 ~ms ⁻¹ ) Correct option: (1)