Sample QuestionsNuclei questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two nuclei have their mass numbers in the ratio of 1:27. The ratio of their nuclear densities are-
- A
$1: 27$
- ✓
$1: 1$
- C
$1: 3$
- D
$1: 9$
Answer: B.
View full solution →If the binding energy per nucleon for 3Li7 is 5.6MeV, the total binding energy of a lithium nucleus is?
In an endothermic reaction the binding energies of reactants and products are e1, e2 respectively, then:
The difference between the mass of a nucleus and the total mass of the constituents is its.
The mass number of a nucleus is equal to:
- A
The number of neutrons in the nucleus.
- B
The number of protons in the nucleus.
- C
The number of nucleons in the nucleus.
- D
View full solution →For question, statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a) (b) (c) and (d) as given below.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is NOT the correct explanation of A.
- A is true, but R is false.
- A is false and R is also false.
Assertion (A): $_7^{14}\text{N}$ is stable.
Reason (R): Nuclei having an odd number of protons and an odd number of neutrons are generally less stable than the one having even number of protons and even number of neutrons.
View full solution →For question, statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a) (b) (c) and (d) as given below.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is NOT the correct explanation of A.
- A is true, but R is false.
- A is false and R is also false.
Assertion (A): Density of all the nuclei is same.
Reason (R): Radius of nucleus is directly proportional to the cube root of mass number.
For question, statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a) (b) (c) and (d) as given below.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is NOT the correct explanation of A.
- A is true, but R is false.
- A is false and R is also false.
Assertion (A): Energy is released in a nuclear reaction.
Reason (R): In any nuclear reaction the reactants and resultant products obey the law of conservation of charge and mass only.
For question, statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a) (b) (c) and (d) as given below.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is NOT the correct explanation of A.
- A is true, but R is false.
- A is false and R is also false.
Assertion (A): A fission reaction can be more easily controlled than a fission reaction.
Reason (R): The percentage of mass converted to energy in a fission reaction is 0.1% whereas in a fission reaction it is 0.4%
For question, statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a) (b) (c) and (d) as given below.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is NOT the correct explanation of A.
- A is true, but R is false.
- A is false and R is also false.
Assertion (A): Nuclear density is extremely higher than atomic density.
Reason (R): Most of the mass of the atom is concentrated in the nucleus.
Calculate the energy equivalent of $1 g$ of substance.
View full solution →Given the mass of iron nucleus as $55.85 u$ and $A =56$, find the nuclear density?
View full solution →Why is it found experimentally difficult to detect neutrinos in nuclear $\beta$-decay?
View full solution →Define the activity of a given radioactive substance. Write its S.I. unit.
Write any two characteristic properties of nuclear force.
Suppose, we think of fission of a $^{56}_{26}\text{Fe}$ nucleus into two equal fragments, $^{28}_{13}\text{Al}.$ Is the fission energetically possible? Argue by working out Q of the process. Given $\text{m}(^{56}_{26}\text{Fe})=55.93494\text{ u and m }(^{28}_{13}\text{Al})=27.98191\text{ u}.$
View full solution →Two stable isotopes of lithium $^6_3\text{Li }\text{ and }\ ^7_3\text{Li}$ have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.
View full solution →The three stable isotopes of neon: $^{20}_{10}\text{Ne},\ ^{21}_{10}\text{Ne }\text{ and }\ ^{22}_{10}\text{Ne}$ have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.
View full solution →The half-life of $^{90}_{38}\text{Sr}$ is 28 years. What is the disintegration rate of 15 mg of this isotope?
View full solution →Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV. Using this, express the mass defect of ${ }_8^{16} O$ in $MeV / c ^2$.
View full solution →Find the Q-value and the kinetic energy of the emitted α-particle in the $\alpha $-decay of - $^{226}_{88}\text{Ra}$ and
- $^{220}_{86}\text{Rn}.$
Given
$\text{m}(^{226}_{88}\text{Ra})=226.02540\text{ u}.$ $\text{m}(^{222}_{86}\text{Rn})=222.01750\text{ u}.$
$\text{m}(^{222}_{86}\text{Rn})=220.01137\text{ u}.$ $\text{m}(^{216}_{84}\text{Po})=216.00189\text{ u}.$
View full solution →The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive $ ^{14}_6\text{C}$ present with the stable carbon isotope $^{12}_6\text{C}.$ When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life (5730 years) of $^{14}_6\text{C },$ and the measured activity, the age of the specimen can be approximately estimated. This is the principle of $^{14}_6\text{C}$ datingused in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.
View full solution →The radionuclide 11C decays according to
$^{11}_{6}\text{C}\rightarrow^{11}_{5}\text{B}+\text{e}^{+}+\text{v}:\ \text{T}_{1/2}=20.3 \text{ min}$
The maximum energy of the emitted positron is 0.960 MeV.
Given the mass values:
$\text{m}(^{11}_{6})=10=11.011434\text{ u and m}(^{11}_{6}\text{B})=11.009305\text {u}.$
calculate Q and compare it with the maximum energy of the positron emitted.
View full solution →In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are $^{24}_{12}\text{Mg }23.98504\text{u}),^{25}_{12}\text{Mg }(24.98584\text{u})\text{ and }^{26}_{12}\text{Mg }(25.98259\text{u}).$ The natural abundance of $^{24}_{12}\text{Mg}\text{ is }78.99\%$ by mass. Calculate the abundances of other two isotopes.
View full solution →A 1000 MW fission reactor consumes half of its fuel in 5.00 y. How much $^{235}_{92}\text{U}$ did it contain initially? Assume that the reactor operates 80% of the time, that all the energy generated arises from the fission of $^{235}_{92}\text{U}$ and that this nuclide is consumed only by the fission process.
View full solution → For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents to get a medical check-up of Radha. The doctor thoroughly examined Radha and diagnosed that she has a brain tumour.
- What, according to you, are the values displayed by Aarti?
- How can radioisotopes help a doctor to diagnose brain tumour?
For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents to get a medical check-up of Radha. The doctor thoroughly examined Radha and diagnosed that she has a brain tumour.
- What, according to you, are the values displayed by Aarti?
- How can radioisotopes help a doctor to diagnose brain tumour?
For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents to get a medical check-up of Radha. The doctor thoroughly examined Radha and diagnosed that she has a brain tumour.
- What, according to you, are the values displayed by Aarti?
- How can radioisotopes help a doctor to diagnose brain tumour?
Why is it found experimentally difficult to detect neutrinos in nuclear $\beta$-decay?
View full solution →When subatomic particles undergo reactions, energy is conserved, but mass is not necessarily conserved. However, a particle's mass “contributes” to its total energy, in accordance with Einstein's famous equation, E = mc
2 In this equation, E denotes the energy carried by a particle because of its mass. The particle can also have additional energy due to its motion and its interactions with other particles. Consider a neutron at rest and well separated from other particles. It decays into a proton, an electron and an undetected third particle as given here: Neutron → proton + electron + ??? The given table summarizes some data from a single neutron decay. Electron volt is a unit of energy. Column 2 shows the rest mass of the particle times the speed of light squared.
| Particle | Mass × c2 (MeV) | Kinetic energy (MeV) |
| Neutron | 940.97 | 0.00 |
| Proton | 939.67 | 0.01 |
| Electron | 0.51 | 0.39 |
- From the given table, which properties of the undetected third particle can be calculate?
- Total energy, but not kinetic energy.
- Kinetic energy, but not total energy.
- Both total energy and kinetic energy.
- Neither total energy nor kinetic energy.
- Assuming the table contains no major errors, what can we conclude about the (mass × c2) of the undetected third particle?
- It is 0. 79 MeV
- It is 0.39 MeV
- It is less than or equal to 0.79 MeV; but we cannot be more precise.
- It is less than or equal to 0.40 MeV; but we cannot be more precise.
- Could this reaction occur?
Proton → neutron + other particles
- Yes, if the other particles have much more kinetic energy than mass energy.
- Yes, but only if the proton has potential energy (due to interactions with other particles).
- No, because a neutron is more massive than a proton.
- No, because a proton is positively charged while a neutron is electrically neutral.
- How much mass has to be converted into energy to produce electric power of 500MW for one hour?
- 2 × 10-5kg
- 1 × 10-5kg
- 3 × 10-5kg
- 4 × 10-5kg
- The equivalent energy of 1g of substance is.
- 9 × 1013J
- 6 × 1012J
- 3 × 1013J
- 6 × 1013J
Consider the D–T reaction (deuterium–tritium fusion) $^2_1\text{H}+^3_1\text{H}\rightarrow^4_2\text{He}+\text{n} $ - Calculate the energy released in MeV in this reaction from the data:
$\text{m}(^2_1\text{H})=2.014102\text{ u}$
$\text{m}(^3_1\text{H})=3.016049\text{ u}$
- Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction? (Hint: Kinetic energy required for one fusion event =average thermal kinetic energy available with the interacting particles = 2(3kT/2); k = Boltzman’s constant, T = absolute temperature.)
View full solution →A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to
- 3.125%,
- 1% of its original value?
Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of $^{235}\text{U}$ in a fission reactor.
View full solution →Under certain circumstances, a nucleus can decay by emitting a particle more massive than an $\alpha$particle. Consider the following decay processes:
$^{223}_{88}\text{Ra}\rightarrow^{209}_{82}\text{Pb}+^{14}_{6}\text{C}$
$^{223}_{88}\text{Ra}\rightarrow^{219}_{86}\text{Rn}+^{4}_{2}\text{He}$
Calculate the Q-values for these decays and determine that both are energetically allowed.
View full solution →Consider the fission of $^{238}_{92}\text{U}$ by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are $^{140}_{58}\text{Ce}$ and $^{99}_{44}\text{Ru}.$ Calculate Q for this fission process.
The relevant atomic and particle masses are:
$\text{m}(^{238}_{92}\text{U})=238.05079\text{ u}$
$\text{m}(^{140}_{58}\text{Ce})=139.90543\text{ u}$
$\text{m}(^{99}_{44}\text{Ru})=98.90594\text{ u}$
View full solution →