Exams › JEE Main › Physics

For a radioactive nucleus, which expression correctly connects the mean life (t_av) with the half-life (t₁/2)?

1. t_av = t₁/2
2. t_av = ½ t₁/2
3. 0.693 t_av = t₁/2
4. t_av = 0.693 t₁/2

Correct answer: 0.693 t_av = t₁/2

Solution

The mean life of a radioactive nucleus is related to its half-life by the factor of 0.693, which is derived from the exponential decay formula. This means that the mean life is approximately 0.693 times the half-life, making option C the correct expression.

Related JEE Main Physics questions

• A radioactive specimen has activity R1 at time T1 and activity R2 at time T2. If its half-life is T, then the number of atoms decayed during the interval (T1 - T2) is proportional to
• Which one of the following statements is true?
• A nucleus splits into two fragments, and the speeds of the fragments are in the ratio 2:1. What is the ratio of their nuclear radii?
• If M(A, Z), Mₚ and Mₙ represent, respectively, the mass of the nucleus ^(A)_(Z)X, the proton mass and the neutron mass, all expressed in atomic mass units (1 u = 931.5 MeV/c²), and BE denotes the binding energy in MeV, which relation is correct?
• As the number of nucleons in a nucleus increases, how does the binding energy per nucleon change?
• A radioactive nucleus decays through the sequence A --α--> A1 --β--> A2 --α--> A3 --γ--> A4. If nucleus A has mass number 180 and atomic number 72, what are the mass number and atomic number of A4?

⚔️ Practice JEE Main Physics free + battle 1v1 →