Question

Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of log_e (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).
(D) Product of decay constant (λ) and half-life time (T_1/2) is not constant.
Choose the most appropriate answer from the options given below:

• (A) and (B) only
• (B) and (D) only
• (B) and (C) only
• (C) and (D) only

Answer 1

The Correct Option is C

Radioactive decay is a random and spontaneous process it depends on unbalancing of nucleus.
N = N₀e^–λt …(B)
ln N = –λt + lnN₀
So, slope = – λ …(C)
t_1/2=\(\frac{ln2}{lλ}\)
So t_1/2 × λ = ln2 = Constant