A heavy nucleus N,at rest,undergoes fission N | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A,C,D) The fission reaction is $N \rightarrow P + Q$. The energy released in the fission process is given by the mass defect $\delta$ multiplied by $

Vedclass · Accepted Answer

$A, C, D$

Vedclass · Answer

(A,C,D) The fission reaction is $N \rightarrow P + Q$. The energy released in the fission process is given by the mass defect $\delta$ multiplied by $c^2$,which is $E = \delta c^2$.Since the initial nucleus $N$ is at rest,the total energy released is converted into the kinetic energies of the product nuclei $P$ and $Q$. Thus,$E_P + E_Q = \delta c^2$. Statement $(A)$ is correct.By the law of conservation of linear momentum,the initial momentum is zero,so the magnitudes of the momenta of $P$ and $Q$ must be equal: $p_P = p_Q = p$. Thus,$M_P v_P = M_Q v_Q$,which implies $\frac{v_P}{v_Q} = \frac{M_Q}{M_P}$. Statement $(C)$ is correct.The kinetic energy is given by $E = \frac{p^2}{2M}$. Since $p_P = p_Q = p$,we have $E_P = \frac{p^2}{2M_P}$ and $E_Q = \frac{p^2}{2M_Q}$.Substituting these into the energy equation: $\frac{p^2}{2M_P} + \frac{p^2}{2M_Q} = \delta c^2$.$\frac{p^2}{2} \left( \frac{M_Q + M_P}{M_P M_Q} \right) = \delta c^2$.Using the reduced mass $\mu = \frac{M_P M_Q}{M_P + M_Q}$,we get $\frac{p^2}{2\mu} = \delta c^2$,which gives $p = c \sqrt{2 \mu \delta}$. Statement $(D)$ is correct.Statement $(B)$ is incorrect because $E_P = \frac{p^2}{2M_P} = \frac{2\mu \delta c^2}{2M_P} = \frac{M_Q}{M_P+M_Q} \delta c^2$.

Similar Questions

$A$ nuclear reactor provides power of $300 \, MW$. If $170 \, MeV$ of energy is released per fission of a $U^{235}$ nucleus, then the number of uranium atoms undergoing fission per hour is:

Assertion: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
Reason: For heavy nuclei,binding energy per nucleon increases with increasing $Z$,while for light nuclei,it decreases with increasing $Z$.

In the nuclear fusion reaction $_1^2H + _1^3H \to _2^4He + n$,given that the repulsive potential energy between the two nuclei is $7.7 \times 10^{-14} \ J$,the temperature at which the gases must be heated to initiate the reaction is nearly? [Boltzmann's constant $k = 1.38 \times 10^{-23} \ J/K$]

Energy released in the fission of a single $_{92}U^{235}$ nucleus is $200 \, MeV$. The fission rate of a $_{92}U^{235}$ fuelled reactor operating at a power level of $5 \, W$ is

In a nuclear reactor,boron rods are used as ...... .

Vedclass Test Series

Exam Paper Generator

Online Exam Module