Physics MCQs for NEET — Practice Questions with Answers

3.  Production of more neutrons in fission

$$\begin{gathered} \left(3\right) \\ \mathrm{Density} = \frac{\mathrm{mass}}{\mathrm{volume}} \\ = \frac{\mathrm{A}{M}_p}{{\displaystyle \frac{4}{3}}{\mathrm{\pi R}}_0^3\mathrm{A}} [M_p : Mass of a nucleon] \\ So density is independent of A \end{gathered}$$

Fon heavier nuclei, binding energy per nucleon is minimum.

$$\begin{gathered} \left(4\right) \\ {}_1\mathrm{H}_2 + {}_1\mathrm{H}_2 \to {}_2\mathrm{He}_2 \\ \mathrm{B}.\mathrm{E}. \mathrm{of} \mathrm{reactant} \\ = 2 \mathrm{x} 1.1 \mathrm{x} 2 \\ = 4.4 \mathrm{MeV} \\ \mathrm{B}.\mathrm{E}. \mathrm{of} \mathrm{product} = 7.0 \mathrm{x} 4 \\ = 28.0 \mathrm{MeV} \\ \mathrm{Energy} \mathrm{released} = 28.0 - 4.4 \\ = 23.6 \mathrm{MeV} \end{gathered}$$

$$\begin{gathered} \left(3\right) \\ 2000 = 16000{\left(\frac{1}{2}\right)}^n \\ \mathrm{n} = 3 \\ {\mathrm{T}}_{\mathrm{H}} = \frac{12}{3} = 4 \end{gathered}$$

Conceptual

α-particles are charged particles, so they can deflect by electric field.

(b) Let initial number of nuclei in A and B is $N_O$

Number of nuclei of A after time t is 

               $N_A=N_{0e^{-8\lambda t}}$                          ...(i)

Similarly, number of nuclei of A after time t is   

             $N_B=N_0{e}^{-\lambda t}$                          ...(ii)

It is given that 

$\frac{N_A}{N_B}=\frac{1}{e} \left|\therefore N_B>N_A\right|$

Now,from Eqs.(i)  and (ii)

$\frac{e^{-B\lambda t}}{e^{-\lambda t}}=\frac{1}{e}$

Rearranging 

$\Rightarrow e^{-1}=e^{-7\lambda t} \Rightarrow 7\lambda t=1$

$\Rightarrow Time \left(t\right)=\frac{1}{7\lambda }$

(d) Key idea Half-life of a radioactive substance is $T_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$\propto$log $\left(\frac{N_o}{N}\right)$

Given,     $$\begin{gathered} N_1=0.6N_{0 } \left(\because 40\% decay\right) \\ {N}_2=0.15N_{0 } \left(\because 85\% decay\right) \end{gathered}$$

Putting these in the formula

        $\frac{N_2}{N_1}=\frac{0.15N_0}{0.6N_0}=\frac{1}{4}={\left(\frac{1}{2}\right)}^2$

So, two half-life periods has passed.

Thus, time taken=2$\times t_{1/2}=2\times 30=60$ min

(b)

 $$\begin{gathered} Radius of nucleus is given by- \\ R=R_0{A}^{1/3} \\ \Rightarrow R \alpha A^{1/3} \\ \frac{R_{Al}}{R_{Te}}={\left(\frac{27}{125}\right)}^{1/3}=\frac{3}{5} \\ \Rightarrow R_{Te}=\frac{5}{3}{R}_{Al} \end{gathered}$$