Energetics of Nuclear Fission

Q. The following figure represents the liquid drop model of nuclear fission. The energies of these states are $E_1,E_{2}and{E}_3$ respectively. Which option is correct?

1. $E_1>E_2<E_3$
2. $E_1>E_2>E_3$
3. $E_1<E_2<E_3$
4. $E_1<E_2>E_3$

Q. Statement I: Nuclear fission is not a spontaneous process as the energy is required to be supplied to it to reach the intermediate state before breaking up into two fragments.
Statement II: The energy of the intermediate state is higher than the initial energy of the parent nucleus.

1. Both the statements are correct and statement II infers to statement I
2. Both the statements are correct but statement II doesn’t infer to statement I
3. Statement I is correct but statement II is incorrect
4. Statement II is correct but statement I is incorrect

Q. In the given radioactive disintegration series,
${}_{92}^{235}U{\to }_{82}^{207}Pb$
Calculate the difference between the number of $\alpha$ and $\beta$ particles emitted in this series.

Q. 15. The radio active " Sr that is formed due to nuclear explosion has half life { period of 28.1 years. In the body of a child born at this time 90Sr is found to { be 10^{-6 gram, then what will be ^{90Sr destroyed from the body of child when the { age of the child will be 30 years.

Q. A heavier unstable nucleus breaks into two fragments of comparable mass in a nuclear fission reaction and energy is released because:

1. The total rest mass energy of the two fragments is less than the rest mass energy of the heavy nucleus.
2. The binding energy per nucleon of the two fragments is more than the binding energy per nucleon of the heavy nucleus.
3. The nuclei of the fragments are more bound than the nucleus of the parent.
4. NONE OF THE ABOVE

Q. Liquid hydrogen is used as a fuel for rocket propulsion.

1. True
2. False

Q. Statement I : Nuclear fission is a spontaneous process, i.e., there is no need of external energy supply for this to happen.
Statement II : In a nuclear fission reaction, the rest mass energy of the parent nucleus is more than the combined rest mass energy of two daughter fragments and neutrons.

1. Statement II is correct but statement I is incorrect
2. Statement I is correct but statement II is incorrect
3. Both the statements are correct and statement II infers to statement I
4. Both the statements are correct but statement II doesn’t infer to statement I

Q. Assume a hypothetical nuclear fission reaction:
$X\to Y+Z$
If the atomic masses of $X,YandZ$ are respectively $x,yandz$ calculate the maximum amount of heat generated if 1gramof X undergoes fission. Consider the molar mass of X to be M.

1. $\frac{N_A}{M}\times (y-z-x)c^{2}units$
2. $\frac{N_A}{M}\times (x-y-z)c^{2}units$
3. $\frac{N_A}{M}\times (x-y+z)c^{2}units$
4. $M\times (x-y-z)c^{2}units$

Q. A heavier unstable nucleus breaks into two fragments of comparable mass in a nuclear fission reaction and energy is released because:

1. The total rest mass energy of the two fragments is less than the rest mass energy of the heavy nucleus.
2. The binding energy per nucleon of the two fragments is more than the binding energy per nucleon of the heavy nucleus.
3. The nuclei of the fragments are more bound than the nucleus of the parent.
4. NONE OF THE ABOVE

Q. The activity of the radioactive sample drops to 1 / 64 of its original value in 2 hr find the decay constant ?$\left(\lambda \right).$

1. $\left(\lambda \right)=1.079h{r}^{-1}$
2. $\left(\lambda \right)=2.579h{r}^{-1}$
3. $\left(\lambda \right)=1.579h{r}^{-1}$
4. $\left(\lambda \right)=2.079h{r}^{-1}$

Q. Which of the following ratio will give stability to daughter element, when radioactive parent element has less number of protons compared to number of neutrons?

1. $\frac{N+1}{Z+1}$
2. $\frac{N-1}{Z+1}$
3. $\frac{N-1}{Z-1}$
4. $\frac{N+1}{Z-1}$

Q. The half life of a radioactive isotope is $3$ hours. What is the value of its disintegration constant?

1. $0.231mi{n}^{-1}$
2. $0.231hou{r}^{-1}$
3. $0.3hou{r}^{-1}$
4. $0.693hou{r}^{-1}$

Q. Shown here are the steps of nuclear fission using the liquid drop model. Which of these is the correct sequence?

1. b, c, a
2. b, a, c
3. c, b, a
4. a, b, c

Q. In the given radioactive disintegration series,
${}_{92}^{235}U{\to }_{82}^{207}Pb$
Calculate the difference between the number of $\alpha$ and $\beta$ particles emitted in this series.

Q. A radioactive isotope is being produced at a constant rate of $dN/dt=R$ in an experiment. The isotope has a half-life of $t_{1/2}$. After a time $t>>t_{1/2}$, the number of active nuclei will become constant. The value of this constant is :

1. $R$
2. $1$
3. $R/\lambda$
4. $\lambda /R$

Q. A radioactive sample had an initial activity of 56 DPM ( disintegration per min ). After 69.3 min, it was found to have an activity of 28 DPM. Find the number of atoms in a sample having an activity of 10 DPM.

1. 693
2. 1000
3. 100
4. 10, 000

Q. After $20$ min, the amount of certain radioactive substance disintegrate was $(15/16{)}^{th}$ of the original amount.

1. $7$
2. $4$
3. $5$
4. $10$

Q. The unit for nuclear dose given to a patient is

1. Fermi
2. Rutherford
3. Curie
4. Roentgen

Q. The disintegration rate for a sample containing ${}_{27}^{60}Co$ as the only radioactive nuclide, is found to be $240$ atoms/ minute. $t_{1/2}$ of $Co$ is $5.2$ years. Find the number of atoms of $Co$ in the sample. How long must this radioactive sample be maintained before the rate falls to $100$ disintegration / minute.

Q. Shown here are the steps of nuclear fission using the liquid drop model. Which of these is the correct sequence?

1. b, c, a
2. c, b, a
3. a, b, c
4. b, a, c

Q. $m$ g of a radioactive species (atomic mass $M$) has decay constant $\lambda$. The initial specific activity at zero time is given by :

1. $\lambda \frac{N_A}{M}$
2. $\lambda \frac{N_{A}m}{M}$
3. $\frac{\lambda m}{M}$
4. $mM{e}^{\lambda }$

Q. Concentration of the radioactive element after one average life is _________ of the original concentration.

1. $\frac{1}{2}$
2. $\frac{1}{e}$
3. $\frac{1}{e^2}$
4. none of these

Q. Assertion :In radioactive disintegrations, ${}_2{He}^4$ nuclei can come out of the nucleus but lighter ${}_2{He}^3$ can't. Reason: Binding energy of ${}_2{He}^3$ is more than that of ${}_2{He}^4$.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. In the given radioactive disintegration series,
${}_{92}^{235}U{\to }_{82}^{207}Pb$
Calculate the difference between the number of $\alpha$ and $\beta$ particles emitted in this series.

Q. In the following disintegration
${}_{92}^{238}U⟶{}_{82}^{206}Pb+.......$
number of $\beta$-particles emitted is

1. 6
2. 4
3. 5
4. None of these

Q. In the nuclear change ${}_{92}\mathrm{U}^{235}+{}_{0}n^1$ → Fission products + neutron + 3.20 × 10^–11 J, the energy released when 1 g of ${}_{92}\mathrm{U}^{235}$ finally undergoes fission is
(a) 12.75 ​× 10⁸ kJ (b) 18.60 ​× 10⁹ kJ (c) 8.21 × 10⁷ kJ (d) 6.55 × 10⁶ kJ