Nuclei's Question 8 | Physics XII - Part 2 | NCERT Exemplar Questions

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MCQ (Multiple Correct Answer)

Fusion processes, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact

nuclear forces have short range

nuclei are positively charged

the original nuclei must be completely ionized before fusion can take place

the original nuclei must first break up before combining with each other

MCQ (Multiple Correct Answer)

Samples of two radioactive nuclides $A$ and $B$ are taken $\lambda_A$ and $\lambda_B$ are the disintegration constants of $A$ and $B$ respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?

Initial rate of decay of $A$ is twice the initial rate of decay of $B$ and $\lambda_A=\lambda_B$

Initial rate of decay of $A$ is twice the initial rate of decay of $B$ and $\lambda_A>\lambda_B$

Initial rate of decay of $B$ is twice the initial rate of decay of $A$ and $\lambda_A>\lambda_B$

Initial rate of decay of $B$ is same as the rate of decay of $A$ at $t=2 \mathrm{~h}$ and $\lambda_B<\lambda_A$

MCQ (Multiple Correct Answer)

The variation of decay rate of two radioactive samples $A$ and $B$ with time is shown in figure. Which of the following statements are true?

Decay constant of $A$ is greater than that of $B$, hence $A$ always decays faster than $B$

Decay constant of $B$ is greater than that of $A$ but its decay rate is always smaller than that of $A$

Decay constant of $A$ is greater than that of $B$ but it does not always decay faster than $B$

Decay constant of $B$ is smaller than that of $A$ but still its decay rate becomes equal to that of $A$ at a later instant

Subjective

$\mathrm{He}_2^3$ and $\mathrm{He}_1^3$ nuclei have the same mass number. Do they have the same binding energy?

Explanation

Nuclei $\mathrm{He}_2^3$ and $\mathrm{He}_1^3$ have the same mass number. $\mathrm{He}_2^3$ has two proton and one neutron. $\mathrm{He}_1^3$ has one proton and two neutron. The repulsive force between protons is missing in ${ }_1 \mathrm{He}^3$ so the binding energy of ${ }_1 \mathrm{He}^3$ is greater than that of ${ }_2 \mathrm{He}^3$.

Subjective

Draw a graph showing the variation of decay rate with number of active nuclei.

Explanation

We know that, rate of decay $=\frac{-d N}{d t}=\lambda N$

where decay constant $(\lambda)$ is constant for a given radioactive material. Therefore, graph between $N$ and $\frac{d N}{d t}$ is a straight line as shown in the diagram.

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