Q78 / 90 · JEE Main 2022 (26 Jun Shift 2) · Physics

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective halflife of the nucleus will be

  • A
    3.75 hours
  • B
    0.56 hours
  • C
    0.26 hours
  • Correct answer
    D
    1.80 hours

Solution

Here the particle is decayed by two processes with decay constant λ1 and λ2.

  Figure

Radioactive decay rate is directly proportional to number of nucleus present at any time, so total rate of decay is 

dAdt--λ1A+-λ2A

⇒dAdt=-λ1+λ2A

⇒λeff =λ1+λ2

⇒ln2t12eff=ln2t121+ln2t122

⇒t12off =4.5×37.5 hours =1.8 hours

Hence, the correct answer is option: 'D'.

Relevant Questions