Easy MCQ +4 / -1 PYQ · JEE Mains 2022

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 loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ($\tau$).

(D) Product of decay constant ($\lambda$) and half-life time (T1/2) is not constant.

Choose the most appropriate answer from the options given below :

  1. A (A) and (B) only
  2. B (B) and (D) only
  3. C (B) and (C) only Correct answer
  4. D (C) and (D) only

Solution

<p>Radioactive decay is a random and spontaneous process it depends on unbalancing of nucleus.</p> <p>$N = {N_0}{e^{ - \lambda t}}$ ..... (B)</p> <p>$\ln N = - \lambda t + \ln {N_0}$</p> <p>So, slope $= - \lambda$ ..... (C)</p> <p>${t_{1/2}} = {{\ln 2} \over \lambda }$</p> <p>So ${t_{1/2}} \times \lambda = \ln 2 =$ Constant</p>

About this question

Subject: Physics · Chapter: Atoms and Nuclei · Topic: Bohr's Model of Hydrogen Atom

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