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

Concepts of Physics - Vol. 2

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

Concepts of Physics - Vol. 2 - Shaalaa.com

Chapter 24: The Nucleus

Short AnswersMCQOthers

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

Short Answers | Q 1 | Page 440

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

Short Answers | Q 2 | Page 440

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?

Short Answers | Q 3 | Page 440

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?

Short Answers | Q 4 | Page 440

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

Short Answers | Q 5 | Page 440

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

Short Answers | Q 6 | Page 440

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?

Short Answers | Q 7 | Page 440

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

Short Answers | Q 8 | Page 440

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

Short Answers | Q 9 | Page 440

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?

Short Answers | Q 10 | Page 440

Does a nucleus lose mass when it suffers gamma decay?

Short Answers | Q 11 | Page 440

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? 

Short Answers | Q 12 | Page 440

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]

MCQ | Q 1 | Page 440

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.

MCQ | Q 2 | Page 440

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.

MCQ | Q 3 | Page 440

As compared to 12C atom, 14C 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

MCQ | Q 4 | Page 440

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.

MCQ | Q 5 | Page 440

The graph of ln(R/R0) versus ln A(R = radius of a nucleus and A = its mass number) is

  • a straight line

  • a parabola

  • an ellipse

  • none of them.

MCQ | Q 6 | Page 440

Let Fpp, Fpn and Fnn 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.

  • Fpp > Fpn = Fnn

  • Fpp = Fpn = Fnn

  • Fpp > Fpn > Fnn

  • Fpp < Fpn = Fnn

MCQ | Q 7 | Page 440

Let Fpp, Fpn and Fnn 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.

  • Fpp > Fpn = Fnn

  • Fpp = Fpn = Fnn

  • Fpp > Fpn > Fnn

  • Fpp < Fpn = Fnn

MCQ | Q 8 | Page 440

Two protons are kept at a separation of 10 nm. Let Fn and Fe be the nuclear force and the electromagnetic force between them.

  • Fe = Fn

  • Fe >> Fn

  • Fe << Fn

  • Fe and Fn differ only slightly.

MCQ | Q 9 | Page 441

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.

MCQ | Q 10 | Page 441

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.

MCQ | Q 11 | Page 441

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.

MCQ | Q 12 | Page 441

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

MCQ | Q 13 | Page 441

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.

MCQ | Q 14 | Page 441

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.

MCQ | Q 15 | Page 441

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.

MCQ | Q 16 | Page 441

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

  • neutron

  • proton

  • electron

  • positron

MCQ | Q 17 | Page 441

Ten grams of 57Co 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

MCQ | Q 18 | Page 441

Free 238U 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.

MCQ | Q 19 | Page 441

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]

MCQ | Q 1 | Page 441

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

  • Mass

  • Volume

  • Density

  • Binding energy

MCQ | Q 2 | Page 441

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.

MCQ | Q 3 | Page 441

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

MCQ | Q 4 | Page 441

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.

MCQ | Q 5 | Page 441

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

  • α-decay

  •  β+-decay

  • β-decay

  • γ-decay

MCQ | Q 6 | Page 441

In which of the following decays the atomic number decreases?

(a) α-decay
(b) β+-decay
(c) β-decay
(d) γ-decay

MCQ | Q 7 | Page 441

Magnetic field does not cause deflection in

  • α-rays

  • beta-plus rays

  •  beta-minus rays

  • gamma rays

MCQ | Q 8 | Page 441

Which of the following are electromagnetic waves?

  •  α-rays

  • Beta-plus rays

  • Beta-minus rays

  • Gamma rays

MCQ | Q 9 | Page 441

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

MCQ | Q 10 | Page 442

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]

Q 1 | Page 442

Assume that the mass of a nucleus is approximately given by M = Amp 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?

Q 2 | Page 442

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 × 1030 kg (twice the mass of the sun).

Q 3 | Page 442

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

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 4 | Page 442

How much energy is released in the following reaction : 7Li + p → α + α.
Atomic mass of 7Li = 7.0160 u and that of 4He = 4.0026 u.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 5 | Page 442

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

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 6 | Page 442

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

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 7 | Page 442

Find the energy liberated in the reaction
223Ra → 209Pb + 14C.
The atomic masses needed are as follows.
223Ra         209Pb        14C
22..018 u  208.981 u  14.003 u

Q 8 | Page 442

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 MZ,N = mass of an atom with Z protons and N neutrons in the nucleus and MB = mass of a hydrogen atom. This energy is known as proton-separation energy.

Q 9 | Page 442

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

Q 10 | Page 442

32P beta-decays to 32S. 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 32P = 31.974 u and that of 32S = 31.972 u.

Q 11 | Page 442

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.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 12 | Page 442

Complete the following decay schemes.

(a) `"" _88^226Ra → alpha+`

(b) `""_8^19O → _9^19F+`

(c) `""_13^25Al → ""_12^25Mg+`

Q 13 | Page 442

In the decay 64Cu → 64Ni + 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.

Q 14 | Page 442

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.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 15 | Page 442

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

Q 16 | Page 442

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

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 17 | Page 442

28Th emits an alpha particle to reduce to 224Ra. 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 228Th is 228.028726 u, that of 224Ra is 224.020196 u and that of  `""_2^4H` is 4.00260 u.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 18 | Page 442

Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:
12N → 12C* + e+ + v
12C* → 12C + γ (4.43MeV).
The atomic mass of 12N is 12.018613 u.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 19 | Page 442

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?

Q 20 | Page 443

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

Q 21 | Page 443

Radioactive 131I has a half-life of 8.0 days. A sample containing 131I 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?

Q 22 | Page 443

The decay constant of 238U is 4.9 × 10−18 S−1. (a) What is the average-life of 238U? (b) What is the half-life of 238U? (c) By what factor does the activity of a 238U sample decrease in 9 × 109 years?

Q 23 | Page 443

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?

Q 24 | Page 443

The count rate from a radioactive sample falls from 4.0 × 106 per second to 1.0 × 106per second in 20 hours. What will be the count rate 100 hours after the beginning?

Q 25 | Page 443

The half-life of 226Ra is 1602 y. Calculate the activity of 0.1 g of RaCl2 in which all the radium is in the form of 226Ra. Taken atomic weight of Ra to be 226 g mol−1 and that of Cl to be 35.5 g mol−1.

Q 26 | Page 443

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.

Q 27 | Page 443

The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old 32P(t1/2 = 14.3 days) source if it was originally purchased for 800 rupees?

Q 28 | Page 443

57Co decays to 57Fe by β+- emission. The resulting 57Fe 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 57Co gives 5.0 × 109 gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 109per second?

Q 29 | Page 443

Carbon (Z = 6) with mass number 11 decays to boron (Z = 5). (a) Is it a β+-decay or a βdecay? (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?

Q 30 | Page 443

4 × 1023 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.

Q 31 | Page 443

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 cm2 window. If the source contains 6.0 × 1016 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.

Q 32 | Page 443

238U decays to 206Pb with a half-life of 4.47 × 109 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 238U and 0.600 mg of 206Pb. Assuming that all the lead has come from uranium, find the life of the rock.

Q 33 | Page 443

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

Q 34 | Page 443

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.

Q 35 | Page 443

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

Time t (minute): 0 25 50 75 100
Ctount rate R (109 s−1): 30 16 8.0 3.8 2.0

(a) Plot In (R0/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 t1/2.

Q 36 | Page 443

The half-life of 40K is 1.30 × 109 y. A sample of 1.00 g of pure KCI gives 160 counts s−1. Calculate the relative abundance of 40K (fraction of 40K present) in natural potassium.

Q 37 | Page 443

`""_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 × 107s−1/2 and b = 1 to find the wavelength of the Kα X-ray emitted following the electron capture.

Q 38 | Page 443

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t1/2. Show that after a time t >> t1/2 the number of active nuclei will become constant. Find the value of this constant.

Q 39 | Page 443

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.

Q 40 | Page 443

In an agricultural experiment, a solution containing 1 mole of a radioactive material (t1/2= 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?

Q 41 | Page 443

A vessel of volume 125 cm3 contains tritium (3H, t1/2 = 12.3 y) at 500 kPa and 300 K. Calculate the activity of the gas.

Q 42 | Page 444

`""_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 212Bi is one hour. If 1 g of pure 212Bi is taken at 12.00 noon, what will be the composition of this sample at 1 P.m. the same day?

Q 43 | Page 444

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

Time (s)

 
Activity (A)
(108 disinte-
grations s−1)
Time (s)

 
Activity (A
108 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/A0) versus time. (b) See that for large values of time, the plot is nearly linear. Deduce the half-life of 110Ag from this portion of the plot. (c) Use the half-life of 110Ag to calculate the activity corresponding to 108Ag in the first 50 s. (d) Plot In (A/A0) versus time for 108Ag for the first 50 s. (e) Find the half-life of 108Ag.

Q 44 | Page 444

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 99Tc. 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?

Q 45 | Page 444

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.

Q 46 | Page 444

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.

Q 47 | Page 444

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

Q 48 | Page 444

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

Q 49 | Page 444

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 235U, at what rate will the amount of 235U decrease? Express your answer in kg per day. (c) Assuming that uranium enriched to 3% in 235U will be used, how much uranium is needed per month (30 days)?

Q 50 | Page 444

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".`

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 51 | Page 444

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.

Q 52 | Page 444

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

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Q 53 | Page 444

Calculate the energy that can be obtained from 1 kg of water through the fusion reaction 2H + 2H → 3H + p. Assume that 1.5 × 10−2% of natural water is heavy water D2O (by number of molecules) and all the deuterium is used for fusion.

(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

Chapter 24: The Nucleus

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

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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.

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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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