#### Chapters

Chapter 2: Kinetic Theory of Gases

Chapter 3: Calorimetry

Chapter 4: Laws of Thermodynamics

Chapter 5: Specific Heat Capacities of Gases

Chapter 6: Heat Transfer

Chapter 7: Electric Field and Potential

Chapter 8: Gauss’s Law

Chapter 9: Capacitors

Chapter 10: Electric Current in Conductors

Chapter 11: Thermal and Chemical Effects of Current

Chapter 12: Magnetic Field

Chapter 13: Magnetic Field due to a Current

Chapter 14: Permanent Magnets

Chapter 15: Magnetic Properties of Matter

Chapter 16: Electromagnetic Induction

Chapter 17: Alternating Current

Chapter 18: Electromagnetic Waves

Chapter 19: Electric Current through Gases

Chapter 20: Photoelectric Effect and Wave-Particle Duality

Chapter 21: Bohr’s Model and Physics of Atom

Chapter 22: X-rays

Chapter 23: Semiconductors and Semiconductor Devices

Chapter 24: The Nucleus

Chapter 25: The Special Theory of Relativity

#### H.C. Verma Concepts of Physics - Vol. 2

## Chapter 24: The Nucleus

#### Chapter 24: The Nucleus Exercise Short Answers solutions [Page 440]

If neutrons exert only attractive force, why don't we have a nucleus containing neutrons alone?

Consider two pairs of neutrons. In each pair, the separation between the neutrons is the same. Can the force between the neutrons have different magnitudes for the two pairs?

A molecule of hydrogen contains two protons and two electrons. The nuclear force between these two protons is always neglected while discussing the behaviour of a hydrogen molecule. Why?

Is it easier to take out a nucleon (a) from carbon or from iron (b) from iron or from lead?

Suppose we have 12 protons and 12 neutrons. We can assemble them to form either a ^{24}Mg nucleus or two ^{12}C nuclei. In which of the two cases more energy will be liberated?

What is the difference between cathode rays and beta rays? When the two are travelling in space, can you make out which is the cathode ray and which is the beta ray?

If the nucleons of a nucleus are separated from each other, the total mass is increased. Where does this mass come from?

In beta decay, an electron (or a positron) is emitted by a nucleus. Does the remaining atom get oppositely charged?

When a boron nucleus `(""_5^10"B")` is bombarded by a neutron, a α-particle is emitted. Which nucleus will be formed as a result?

Does a nucleus lose mass when it suffers gamma decay?

In a typical fission reaction, the nucleus is split into two middle-weight nuclei of unequal masses. Which of the two (heavier or lighter) has greater kinetic energy? Which one has greater liner momentum?

If three helium nuclei combine to form a carbon nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimise the energy?

#### Chapter 24: The Nucleus Exercise MCQ solutions [Pages 440 - 441]

The mass of a neutral carbon atom in ground state is

exact 12 u

less than 12 u

more than 12 u

depends on the form of carbon such as graphite of charcoal.

The mass number of a nucleus is equal to

the number of neutrons in the nucleus

the number of protons in the nucleus

the number of nucleons in the nucleus

none of them.

As compared to ^{12}C atom, ^{14}C atom has

two extra protons and two extra electrons

two extra protons but no extra electrons

two extra neutrons and no extra electron

two extra neutrons and two extra electron

The mass number of a nucleus is

always less than its atomic number

always more than its atomic number

equal to its atomic number

sometimes more than and sometimes equal to its atomic number.

The graph of ln(R/R_{0}) versus ln A(R = radius of a nucleus and A = its mass number) is

a straight line

a parabola

an ellipse

none of them.

Let F_{pp}, F_{pn} and F_{nn} denote the magnitudes of the net force by a proton on a proton, by a proton on a neutron and by a neutron on a neutron respectively. neglect gravitational force. When the separation is 1 fm.

F

_{pp}> F_{pn}= F_{nn}F

_{pp}= F_{pn}= F_{nn}F

_{pp}> F_{pn}> F_{nn}F

_{pp}< F_{pn}= F_{nn}

Let F_{pp}, F_{pn} and F_{nn} denote the magnitudes of the net force by a proton on a proton, by a proton on a neutron and by a neutron on a neutron respectively. neglect gravitational force. When the separation is 1 fm.

F

_{pp}> F_{pn}= F_{nn}F

_{pp}= F_{pn}= F_{nn}F

_{pp}> F_{pn}> F_{nn}F

_{pp}< F_{pn}= F_{nn}

Two protons are kept at a separation of 10 nm. Let F_{n} and F_{e} be the nuclear force and the electromagnetic force between them.

F

_{e}= F_{n}F

_{e}>> F_{n}F

_{e}<< F_{n}F

_{e}and F_{n}differ only slightly.

As the mass number *A* increases, the binding energy per nucleon in a nucleus

increases

decreases

remains the same

varies in a way that depends on the actual value of A.

Which of the following is a wrong description of binding energy of a nucleus?

It is the energy required to break a nucleus into its constituent nucleons.

It is the energy made available when free nucleons combine to form a nucleus.

It is the sum of the rest mass energies of its nucleons minus the rest mass energy of the nucleus.

It is the sum of the kinetic energy of all the nucleons in the nucleus.

In one average-life,

half the active nuclei decay

less than half the active nuclei decay

more than half the active nuclei decay

all the nuclei decay.

In a radioactive decay, neither the atomic number nor the mass number changes. Which of the following particles is emitted in the decay?

Proton

Neutron

Electron

Photon

During a negative beta decay,

an atomic electron is ejected

an electron which is already present within the nucleus is ejected

a neutron in the nucleus decays emitting an electron

a proton in the nucleus decays emitting an electron.

A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

6 h

12 h

24 h

128 h.

The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively

1/λ and (In 2/λ)

(In 2/λ) and 1/λ

λ(In 2) and 1/λ

λ/(In 2) and 1/λ.

An α-particle is bombarded on ^{14}N. As a result, a ^{17}O nucleus is formed and a particle is emitted. This particle is a

neutron

proton

electron

positron

Ten grams of ^{57}Co kept in an open container beta-decays with a half-life of 270 days. The weight of the material inside the container after 540 days will be very nearly

10 g

5 g

2.5 g

1.25 g

Free ^{238}U nuclei kept in a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes *x* in time *t* after the decay. If a decay takes place when the train is moving at a uniform speed *v*, the distance between the alpha particle and the recoiling nucleus at a time *t* after the decay, as measured by the passenger will be

x + vt

x - vt

x

depends on the direction of the train.

During a nuclear fission reaction,

a heavy nucleus breaks into two fragments by itself a light nucleus bombarded by thermal neutrons breaks up

a light nucleus bombarded by thermal neutrons breaks up

a heavy nucleus bombarded by thermal neutrons breaks up

two light nuclei combine to give a heavier nucleus and possible other products.

#### Chapter 24: The Nucleus Exercise MCQ solutions [Pages 441 - 442]

As the mass number *A* increases, which of the following quantities related to a nucleus do not change?

Mass

Volume

Density

Binding energy

The heavier nuclei tend to have larger N/Z ratio because

(a) a neutron is heavier than a proton

(b) a neutron is an unstable particle

(c) a neutron does not exert electric repulsion

(d) Coulomb forces have longer range compared to the nuclear forces.

A free neutron decays to a proton but a free proton does not decay to a neutron. This is because

neutron is a composite particle made of a proton and an electron whereas proton is a fundamental particle

neutron is an uncharged particle whereas proton is a charged particle

neutron has large rest mass than the proton

weak forces can operate in a neutron but not in a proton

Consider a sample of a pure beta-active material.

All the beta particles emitted have the same energy.

The beta particles originally exist inside the nucleus and are ejected at the time of beta decay.

The antineutrino emitted in a beta decay has zero mass and hence zero momentum.

The active nucleus changes to one of its isobars after the beta decay.

In which of the following decays the element does not change?

α-decay

β

^{+}-decayβ

^{−}-decayγ-decay

In which of the following decays the atomic number decreases?

(a) α-decay

(b) β^{+}-decay

(c) β^{−}-decay

(d) γ-decay

Magnetic field does not cause deflection in

α-rays

beta-plus rays

beta-minus rays

gamma rays

Which of the following are electromagnetic waves?

α-rays

Beta-plus rays

Beta-minus rays

Gamma rays

Two lithium nuclei in a lithium vapour at room temperature do not combine to form a carbon nucleus because

a lithium nucleus is more tightly bound than a carbon nucleus

carbon nucleus is an unstable particle

it is not energetically favourable

Coulomb repulsion does not allow the nuclei to come very close

For nuclei with A > 100,

(a) the binding energy of the nucleus decreases on an average as A increases

(b) the binding energy per nucleon decreases on an average as A increases

(c) if the nucleus breaks into two roughly equal parts, energy is released

(d) if two nuclei fuse to form a bigger nucleus, energy is released.

#### Chapter 24: The Nucleus solutions [Pages 442 - 444]

Assume that the mass of a nucleus is approximately given by M = Am_{p} where A is the mass number. Estimate the density of matter in kgm^{−3} inside a nucleus. What is the specific gravity of nuclear matter?

A neutron star has a density equal to that of the nuclear matter. Assuming the star to be spherical, find the radius of a neutron star whose mass is 4.0 × 10^{30} kg (twice the mass of the sun).

Calculate the mass of an α-particle. Its Its binding energy is 28.2 MeV.

(Use Mass of proton m_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

How much energy is released in the following reaction : ^{7}Li + p → α + α.

Atomic mass of ^{7}Li = 7.0160 u and that of ^{4}He = 4.0026 u.

(Use Mass of proton m_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Find the binding energy per nucleon of `""_79^197"Au"` if its atomic mass is 196.96 u.

(Use Mass of proton m_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

(a) Calculate the energy released if ^{238}U emits an α-particle. (b) Calculate the energy to be supplied to ^{238}U it two protons and two neutrons are to be emitted one by one. The atomic masses of ^{238}U, ^{234}Th and ^{4}He are 238.0508 u, 234.04363 u and 4.00260 u respectively.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Find the energy liberated in the reaction^{223}Ra → ^{209}Pb + ^{14}C.

The atomic masses needed are as follows.^{223}Ra ^{209}Pb ^{14}C

22..018 u 208.981 u 14.003 u

Show that the minimum energy needed to separate a proton from a nucleus with Zprotons and N neutrons is `ΔE = (M_(Z-1,N) + M_B - M_(Z,N))c^2`

where M_{Z}_{,N} = mass of an atom with Z protons and N neutrons in the nucleus and M_{B} = mass of a hydrogen atom. This energy is known as proton-separation energy.

Calculate the minimum energy needed to separate a neutron from a nucleus with Zprotons and N neutrons it terms of the masses M_{Z.N}' M_{Z}_{,N−1} and the mass of the neutron.

^{32}P beta-decays to ^{32}S. Find the sum of the energy of the antineutrino and the kinetic energy of the β-particle. Neglect the recoil of the daughter nucleus. Atomic mass of ^{32}P = 31.974 u and that of ^{32}S = 31.972 u.

A free neutron beta-decays to a proton with a half-life of 14 minutes. (a) What is the decay constant? (b) Find the energy liberated in the process.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Complete the following decay schemes.

(a) `"" _88^226Ra → alpha+`

(b) `""_8^19O → _9^19F+`

(c) `""_13^25Al → ""_12^25Mg+`

In the decay ^{64}Cu → ^{64}Ni + e^{+} + *v*, the maximum kinetic energy carried by the positron is found to be 0.650 MeV.

(a) What is the energy of the neutrino which was emitted together with a positron of kinetic energy 0.150 MeV?

(b) What is the momentum of this neutrino in kg m s^{−1}?

Use the formula applicable to a photon.

Potassium-40 can decay in three modes. It can decay by β^{−}-emission, B*-emission of electron capture. (a) Write the equations showing the end products. (b) Find the *Q*-values in each of the three cases. Atomic masses of `""_18^40Ar` , `""_19^40K` and `""_20^40Ca` are 39.9624 u, 39.9640 u and 39.9626 u respectively.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Lithium (*Z* = 3) has two stable isotopes ^{6}Li and ^{7}Li. When neutrons are bombarded on lithium sample, electrons and α-particles are ejected. Write down the nuclear process taking place.

The masses of ^{11}C and ^{11}B are respectively 11.0114 u and 11.0093 u. Find the maximum energy a positron can have in the β*-decay of ^{11}C to ^{11}B.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

^{28}Th emits an alpha particle to reduce to ^{224}Ra. Calculate the kinetic energy of the alpha particle emitted in the following decay:

`""^228"Th" → ""^224"Ra"^(∗) + alpha`

`""^224"Ra"^(∗) → ""^224"Ra" + γ (217 "keV")`.

Atomic mass of ^{228}Th is 228.028726 u, that of ^{224}Ra is 224.020196 u and that of `""_2^4H` is 4.00260 u.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:^{12}N → ^{12}C* + *e*^{+} + *v*^{12}C* → ^{12}C + γ (4.43MeV).

The atomic mass of ^{12}N is 12.018613 u.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

The decay constant of `""_80^197`Hg (electron capture to `""_79^197`Au) is 1.8 × 10^{−4} S^{−1}. (a) What is the half-life? (b) What is the average-life? (c) How much time will it take to convert 25% of this isotope of mercury into gold?

The half-life of ^{199}Au is 2.7 days. (a) Find the activity of a sample containing 1.00 µg of ^{198}Au. (b) What will be the activity after 7 days? Take the atomic weight of ^{198}Au to be 198 g mol^{−1}.

Radioactive ^{131}I has a half-life of 8.0 days. A sample containing ^{131}I has activity 20 µCi at t = 0. (a) What is its activity at t = 4 days? (b) What is its decay constant at t = 4.0 days?

The decay constant of ^{238}U is 4.9 × 10^{−18} S^{−1}. (a) What is the average-life of ^{238}U? (b) What is the half-life of ^{238}U? (c) By what factor does the activity of a ^{238}U sample decrease in 9 × 10^{9} years?

A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample? (b) What is its half-life?

The count rate from a radioactive sample falls from 4.0 × 10^{6} per second to 1.0 × 10^{6}per second in 20 hours. What will be the count rate 100 hours after the beginning?

The half-life of ^{226}Ra is 1602 y. Calculate the activity of 0.1 g of RaCl_{2} in which all the radium is in the form of ^{226}Ra. Taken atomic weight of Ra to be 226 g mol^{−1} and that of Cl to be 35.5 g mol^{−1}.

The half-life of a radioisotope is 10 h. Find the total number of disintegration in the tenth hour measured from a time when the activity was 1 Ci.

The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old ^{32}P(*t*_{1}_{/2} = 14.3 days) source if it was originally purchased for 800 rupees?

^{57}Co decays to ^{57}Fe by β^{+}- emission. The resulting ^{57}Fe is in its excited state and comes to the ground state by emitting γ-rays. The half-life of β^{+}- decay is 270 days and that of the γ-emissions is 10^{−8} s. A sample of ^{57}Co gives 5.0 × 10^{9} gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 10^{9}per second?

Carbon (*Z* = 6) with mass number 11 decays to boron (*Z* = 5). (a) Is it a β^{+}-decay or a β^{−}decay? (b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11?

4 × 10^{23} tritium atoms are contained in a vessel. The half-life of decay tritium nuclei is 12.3 y. Find (a) the activity of the sample, (b) the number of decay in the next 10 hours (c) the number of decays in the next 6.15 y.

A point source emitting alpha particles is placed at a distance of 1 m from a counter which records any alpha particle falling on its 1 cm^{2} window. If the source contains 6.0 × 10^{16} active nuclei and the counter records a rate of 50000 counts/second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window.

^{238}U decays to ^{206}Pb with a half-life of 4.47 × 10^{9} y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of ^{238}U and 0.600 mg of ^{206}Pb. Assuming that all the lead has come from uranium, find the life of the rock.

When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of ^{14}C per gram per minute. A sample from an ancient piece of charcoal shows ^{14}C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of ^{14}C is 5730 y.

Natural water contains a small amount of tritium (`""_1^3H`). This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the `""_1^3H` radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.

The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing ^{128}I varies with time as follows.

Time t (minute): | 0 | 25 | 50 | 75 | 100 |

Ctount rate R (10^{9} s^{−1}): |
30 | 16 | 8.0 | 3.8 | 2.0 |

(a) Plot In (R_{0}/R) against t. (b) From the slope of the best straight line through the points, find the decay constant λ. (c) Calculate the half-life t_{1}_{/2}.

The half-life of ^{40}K is 1.30 × 10^{9} y. A sample of 1.00 g of pure KCI gives 160 counts s^{−1}. Calculate the relative abundance of ^{40}K (fraction of ^{40}K present) in natural potassium.

`""_80^197`Hg decay to `""_79^197`Au through electron capture with a decay constant of 0.257 per day. (a) What other particle or particles are emitted in the decay? (b) Assume that the electron is captured from the K shell. Use Moseley's law √v = a(Z − b) with a = 4.95 × 10^{7}s^{−1}^{/2} and b = 1 to find the wavelength of the K_{α} X-ray emitted following the electron capture.

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

Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at t = 0. Find the number of active nuclei at time t.

In an agricultural experiment, a solution containing 1 mole of a radioactive material (t_{1}_{/2}= 14.3 days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was 1 µCi, what per cent of activity is transmitted from the root to the fruit in steady state?

A vessel of volume 125 cm^{3} contains tritium (^{3}H, t_{1}_{/2} = 12.3 y) at 500 kPa and 300 K. Calculate the activity of the gas.

`""_83^212"Bi"` can disintegrate either by emitting an α-particle of by emitting a β^{−}-particle. (a) Write the two equations showing the products of the decays. (b) The probabilities of disintegration α-and β-decays are in the ratio 7/13. The overall half-life of ^{212}Bi is one hour. If 1 g of pure ^{212}Bi is taken at 12.00 noon, what will be the composition of this sample at 1 P.m. the same day?

A sample contains a mixture of ^{108}Ag and ^{110}Ag isotopes each having an activity of 8.0 × 10^{8} disintegration per second. ^{110}Ag is known to have larger half-life than ^{108}Ag. The activity A is measured as a function of time and the following data are obtained.

Time (s) |
Activity (A) (10 ^{8} disinte-grations s ^{−1}) |
Time (s) |
Activity (A 10 ^{8} disinte-grations s^{−1}) |

20 40 60 80 100 |
11.799 9.1680 7.4492 6.2684 5.4115 |
200 300 400 500 |
3.0828 1.8899 1.1671 0.7212 |

(a) Plot ln (A/A_{0}) versus time. (b) See that for large values of time, the plot is nearly linear. Deduce the half-life of ^{110}Ag from this portion of the plot. (c) Use the half-life of ^{110}Ag to calculate the activity corresponding to ^{108}Ag in the first 50 s. (d) Plot In (A/A_{0}) versus time for ^{108}Ag for the first 50 s. (e) Find the half-life of ^{108}Ag.

A human body excretes (removes by waste discharge, sweating, etc.) certain materials by a law similar to radioactivity. If technetium is injected in some form in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing ^{99}Tc. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is 6 μCi. How much time will elapse before the activity falls to 3 μCi?

A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life τ. Find the value of R for which the ratio of the electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time.

Radioactive isotopes are produced in a nuclear physics experiment at a constant rate dN/dt = R. An inductor of inductance 100 mH, a resistor of resistance 100 Ω and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that i/N remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.

Calculate the energy released by 1g of natural uranium assuming 200 MeV is released in each fission event and that the fissionable isotope ^{235}U has an abundance of 0.7% by weight in natural uranium.

A uranium reactor develops thermal energy at a rate of 300 MW. Calculate the amount of ^{235}U being consumed every second. Average released per fission is 200 MeV.

A town has a population of 1 million. The average electric power needed per person is 300 W. A reactor is to be designed to supply power to this town. The efficiency with which thermal power is converted into electric power is aimed at 25%. (a) Assuming 200 MeV to thermal energy to come from each fission event on an average, find the number of events that should take place every day. (b) Assuming the fission to take place largely through ^{235}U, at what rate will the amount of ^{235}U decrease? Express your answer in kg per day. (c) Assuming that uranium enriched to 3% in ^{235}U will be used, how much uranium is needed per month (30 days)?

Calculate the *Q*-values of the following fusion reactions :-

(a) `""_1^2H + ""_1^2H → ""_1^3H + ""_1^1H`

(b) `""_1^2H + ""_1^2H → ""_2^3H + n`

(c) `""_1^2H + ""_1^3H → _2^4H + n`.

Atomic masses are `m(""_1^2H) = 2.014102 "u", m(""_1^3H) = 3.016049 "u", m(""_2^3He) = 3.016029 "u", m(""_2^4He) = 4.002603 "u".`

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

Calculate the Q-value of the fusion reaction ^{4}He + ^{4}He = ^{8}Be. Is such a fusion energetically favourable? Atomic mass of ^{8}Be is 8.0053 u and that of ^{4}He is 4.0026 u.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Calculate the energy that can be obtained from 1 kg of water through the fusion reaction ^{2}H + ^{2}H → ^{3}H + p. Assume that 1.5 × 10^{−2}% of natural water is heavy water D_{2}O (by number of molecules) and all the deuterium is used for fusion.

_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

## Chapter 24: The Nucleus

#### H.C. Verma Concepts of Physics - Vol. 2

#### Textbook solutions for Class 12

## H.C. Verma solutions for Class 12 Physics chapter 24 - The Nucleus

H.C. Verma solutions for Class 12 Physics chapter 24 (The Nucleus) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Concepts of Physics - Vol. 2 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. H.C. Verma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 12 Physics chapter 24 The Nucleus are Nuclear Force, Controlled Thermonuclear Fusion, Nuclear Reactor, Fission, Introduction of Nuclear Energy, Gamma Decay, Beta Decay, Nuclear Binding Energy, Mass - Energy, Size of the Nucleus, Nuclear Fusion – Energy Generation in Stars, Mass-Energy Relation and Mass Defect, Law of Radioactive Decay, Alpha Decay, Introduction of Radioactivity, Atomic Masses and Composition of Nucleus.

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