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 →Question types
Nuclei question types
454 questions across 7 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
454
Questions
7
Question groups
5
Question types
01
2 Marks Questions
35 Q→023 Marks Question
93 Q→031 Marks Question
26 Q→044 Marks Questions
14 Q→05M.C.Q (1 Marks)
227 Q→06Assertion (A) & Reason (B) MCQ
14 Q→075 Marks Questions
45 Q→Sample Questions
Nuclei questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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 →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 →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 →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 →$^{11}_{6}\text{C}\rightarrow^{11}_{5}\text{B}+\text{e}^{+}+\text{v}:\ \text{T}_{1/2}=20.3 \text{ min}$
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.
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 →From the relation $\text{R}=\text{R}_0\text{A}^{1/3}$ where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).
View full solution →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.
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 →The half-life of 226Ra is 1602y. Calculate the activity of 0.1g of RaCl2 in which all the radium is in the form of 226Ra. Taken atomic weight of Ra to be 226g/mol-1 and that of Cl to be 35.5g/mol-1.
During $\beta^-$ emission:
- AA neutron in the nucleus decays emitting an electron.
- BAn atomic electron is ejected.
- CA part of the binding energy of the nucleus is converted into an electron.
- DA proton in the nucleus decays emitting an electron.
Fusion reaction take place at high temperature because:
- AAtoms are ionized at high temperature.
- BMolecules break up at high temperatures.
- CNuclei break up at high temperature.
- DKinetic energy is high enough to overcome repulsion between nuclei.
Statement-I : Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and
Statement-II: For heavy nuclei, binding energy per nucleon increases with increasing Z. while for light nuclei it decreases with increasing Z.
- ABoth the statements are true and Statement 2 is the correct explanation for Statement 1.
- BBoth the statements are true but Statement 2 is not the correct explanation for Statement 1.
- CStatement 1 is true but Statement 2 is false.
- DStatement 1 is false but Statement 2 is true.
Which of the following isotopes is likely to be most stable?
- A$71\text{Zn}\\30$
- B$66\text{Zn}\\30$
- C$40\text{Ca}\\20$
- DNone of these
Three specimens A, B, C of same radioactive element has activities 1 microcurie, 1 rutherford and 1 becquerel respectively. Which specimen has maximum mass?
- AA
- BB
- CC
- DAll have equal masses.
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.
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 →- 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.
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.
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.
Reason (R): Radius of nucleus is directly proportional to the cube root of mass number.
- 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.
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.
Reason (R): In any nuclear reaction the reactants and resultant products obey the law of conservation of charge and mass only.
- 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.
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.
Reason (R): Most of the mass of the atom is concentrated in the nucleus.
- 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.
Reason (R): Most of the mass of the atom is concentrated in the nucleus.
Obtain the amount of $^{60}_{27}\text{Co}$ necessary to provide a radioactive source of 8.0 mCi strength. The half-life of $^{60}_{27}\text{Co}$ is 5.3 years.
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 →$^{223}_{88}\text{Ra}\rightarrow^{209}_{82}\text{Pb}+^{14}_{6}\text{C}$
$^{223}_{88}\text{Ra}\rightarrow^{219}_{86}\text{Rn}+^{4}_{2}\text{He}$
Calculate the Q-values for these decays and determine that both are energetically allowed.
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 →The relevant atomic and particle masses are:
$\text{m}(^{238}_{92}\text{U})=238.05079\text{ u}$
$\text{m}(^{140}_{58}\text{Ce})=139.90543\text{ u}$
$\text{m}(^{99}_{44}\text{Ru})=98.90594\text{ u}$
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?
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