Mass of helium nucleus$$=4.001265$$ a.m.u; mass of proton $$=1.007277$$ a.m.u. Mass of neutron $$=1.00866$$ a.m.u (take $$1$$ a.m.u$$=931.5$$ MeV)

OR

Calculate the energy released in MeV in the following nuclear reaction

$$^{238}_{92}U \rightarrow ^{234}_{90}Th + ^{4}_{2}He + Q$$

Given Atomic mass of $$^{238}U = 238.05079 \,u$$

Atomic mass of $$^{234}Th = 234.04363 \,u$$

Atomic mass of alpha particle $$= 4.00260 \,u$$

$$1 \,u = 931.5 \,MeV / c^2$$

Is the decay spontaneous ? Give reasons.

Identify the nature of the radioactive radiations emitted in each step of the decay process given below:

$$^{A}_{Z}X \rightarrow ^{A-4}_{Z-1}W$$

A heavy nucleus splits into two lighter nuclei. Which one of the two-parent nucleus or the daughter nuclei has more binding energy per nucleon ?

(1 u = 931.5 MeV/$${ c }^{ 2 }$$, where c is the speed of light in vacuum).

Percentage deviation = $$ \frac {M_{app}M}{M}100$$

(g) Is a value of $$M_{app}$$ accurate enough to be used in a calculation ofa nuclear binding energy?

(a) What is the total of the beta-decay events in the two beta-decay chains?

(b) Calculate $$Q$$ for this fission process. The relevant atomic and particle masses are

$$^{238}U$$ | $$ 238.05079 \ u $$ | $$^{140}Ce$$ | $$ 139.90543 \ u $$ |

$$n$$ | $$ 1.00866 \ u $$ | $$^{99}Ru$$ | $$ 98.90594 \ u $$ |

$$^1H$$ | $$1.007 825 \ u$$ | $$^4He$$ | $$4.002 603 \ u$$ |

$$^2H$$ | $$2.014 102 \ u$$ | $$e^{\pm}$$ | $$0.000 548 6 \ u$$ |

$$^3He$$ | $$3.016 029 \ u$$ |

(Hint: Distinguish carefully between atomic and nuclear masses, and take the positrons properly into account.)

(a) Express this in terms of energy per carbon atom.

(b) Express it in terms of energy per kilogram of the initial reactants, carbon and oxygen.

(c) Suppose that the Sun (mass $$= 2.0 \times 10^{30} \ kg$$) were made of carbon and oxygen in combustible proportions and that it continued to radiate energy at its present rate of $$3.9 \times 10^{26} \ W$$. How long would the Sun last?

In such a fusion energetically favourable? the atomic mass of $$ ^8 Be $$ is 8.0053 u and that of $$ ^4He $$ is 4.0026 u.

$$ ^{223}Ra \rightarrow ^{209}Pb + ^{14}C $$

the atomic masses needed are as follows

$$ ^{223}Ra \quad ^{209}Pb \quad ^{14}C $$

$$ 22.018u \quad 208.981 u \quad 14.003 u $$

Hydrogen bomb is based on the principle of

$$ ^7Li + p \rightarrow \alpha + \alpha $$ tomic mass of $$^Li = 7.0160 u $$ and that of $$ ^He = 4.0026 i=u $$

$$\begin{array}{ll}m(\mathrm{p})=1.007825 \mathrm{u}, & m(\alpha)=4.002603 \mathrm{u} \\m(\mathrm{F})=18.998405 \mathrm{u}, & m(\mathrm{O})=15.994915 \mathrm{u}\end{array}\\$$

Calculate the $$Q$$ of the reaction from these data.

$$^{152} _{63}Eu$$ 151.921 742 u $$^1H$$ 1.007 825 u

n 1.008 665 u

(a) $$^{11}_{6}C \rightarrow ^{z}_{y}B + x + v$$

(b) $$^{12}_{6}C + ^{12}_{6}C \rightarrow ^{20}_{a}Ne + ^{c}_{b}He$$

Find the values of x, y, z and a, b, c.

$${\beta}^{+}$$- decay of $$_{ 43 }^{ 97 }{ Tc }$$

$$\alpha$$- decay of $$_{ 88 }^{ 226 }{ Ra }$$

$${\beta}^{-}$$- decay of $$_{ 83 }^{ 210 }{ Bi }$$

The equation $$E=mc^2$$ is derived by the scientist _________.

In nuclear reactions we have the conservation of ___________.

$$^2_1H\, +\, ^2_1\, \rightarrow\, ^3_2He\, +\, n\, +\, 3.27\, MeV$$.

(ii) Show that the density of nucleus over a wide range of nuclei is constant-independent of mass number $$A$$.

as a function of mass number. Write two important conclusion that can be drawn regarding the nature of nuclear source.

(b) Use this graph to explain the release of energy in both the process of nuclear fusion and fission.

(c) Write the basic nuclear process of neutron undergoing $$\beta $$-decay. why is the detection of neutrinos found very difficult?

$$^{238}_{92}U \rightarrow ^{234}_{90}Th + ^4_2He + energy$$

Determine the energy released in this reaction.

Given: $$m(^{4}_{2}He) = 4.002604\ u$$ and $$m(^{12}_{6}C) = 12.000000\ u$$

(b) Write down the expression for $$Q$$ value in the class of $$\alpha$$ decay.

Mass of proton = 1.00783 u

Mass of neutron = 1.00867 u

Mass of nitrogen nucleus = 14.00307 u

Mass of $$^{20}_{10}Ne=19.992397$$u

Mass of $$^1_1H=1.007825$$u

Mass of $$^1_0n=1.008665$$u.

(b) A radioactive isotope has a half-life of $$10$$ years. How long will it take for the activity to reduce to $$3.125$$%?

(i) Nuclear fission

(ii) Nuclear fusion

(iii) Emission of $$\beta^-$$(i.e., a negative beta particle).

$$\alpha$$- decay of $$_{ 92 }^{ 242 }{ Pu }$$

$$_{ 92 }^{ 298 }{ U\longrightarrow _{ 90 }^{ 234 }{ TH }+_{ 2 }^{ 4 }{ He }+Q }$$

[Mass of $$_{ 92 }^{ 298 }U=238.05079\ u$$ Mass of $$_{ 90 }^{ 234 }{ TH }=234.043630\ u]$$

If 20 N force is applied on a wall which doesn't move the wall than work done by wall is............

$${\beta}^{+}$$- decay of $$_{ 6 }^{ 11 }{ C }$$

Electron capture of $$_{ 54 }^{ 120 }{ Xe }$$

Given masses are $$M(_{ 89 }^{ 236 }{ Ac })=226.028356$$ a.m.u; $$M(_{ 87 }^{ 222 }{ Fr })=222.017415$$a.m.u; $$M(_{ 90 }^{ 236 }{ Th }) =226.017388$$a.m.u; $$M(_{ 88 }^{ 226 }{ Ra })=226.025406$$ a.m.u; $$M(_{ 2 }^{ 4 }{ He })=4.002603$$ a.m.u

$$\ ^{1}H+\ ^{0}Be\rightarrow X+n$$

$$^{259}_{104}Rf$$ 259.105 63 u $$^1H$$ 1.007 825 u

n 1.008 665 u

the second cannot.

Explain.

$$K^0_S \rightarrow \pi^+ + \pi^-$$ (can occur)

$$\wedge^0 \rightarrow \pi^+ + \pi^-$$ (cannot occur)

In the following nuclear reaction

$$n + ^{235}_{92}U \rightarrow ^{144}_{Z}Ba + ^{A}_{36}X + 3n,$$

Assign the values of Z and A.

[Given: $$m\left ( ^{40}_{20}Ca \right ) = 39.962589 \,u$$

$$m_n$$ (mass of a neutron) $$= 1.008665 \,u$$

$$m_p$$ (mass of a proton) $$= 1.007825 \,u$$

$$1 \,u = 931 \,MeV / c^2]$$

Which nuclide out of the two mirror isobars have greater binding energy and why?

$$^{235}_{92}U + ^{1}_{0}n \rightarrow ^{140}_{54} Xe + ^{94}_{34}Sr + 2^{1}_{0}n + Q$$

Given: Mass of $$^{235}_{92}U = 235.0435\,u$$

Mass of $$^{140}_{54}Xe = 139.9054 \,u$$

Mass of $$^{94}_{34}Sr = 93.9063 \,u$$

Mass of $$^{1}_{0}n = 1.00867 \,u$$

$${\beta}^{-}$$- decay of $$_{ 15 }^{ 32 }{ P }$$

$$p+^{15}N\rightarrow _Z^AX+n$$

Find, A, Z and identify the nucleus X.

$$N^{14}+\alpha \rightarrow O^{17}+p$$

The masses of $$N^{14}, He^4, p,$$ and $$O^{17}$$ are, respectively, 14.00307 u, 4.00260 u, 1.00783 u, and 16.99913 u. Find the total kinetic energy of the products if the striking $$\alpha-$$ particle has the minimum kinetic energy required to initiate the reaction:

$$M(_{89}^{226}Ac)=226.028356 amu$$

$$M(_{87}^{222}Fr)=222.017415 amu$$

$$M(_{90}^{226}Th)=226.017388 amu$$

$$M(_{88}^{226}Ra)=226.025406 amu$$

$$M(_2^4He)=4.002603 amu$$

$$p+^{15}N\rightarrow _Z^AX+n$$

Find the Q value of the reaction

$$n+_{92}^{235}U\rightarrow _{92}^{236}U^*\rightarrow _{40}^{99}Ze+_{52}^{134}Te+3n$$

if the neutron is thermal. A thermal neutron is in the thermal equilibrium with its environment; it has an average kinetic energy given by (3/2) kT. Given: $$m(n)=1.0087 amu, M(^{235}U)=235.0439 amu, M(^{99}Zr)=98.916 amu M(^{134}Te)=133.9115 amu$$

(Given: $$1amu=931MeV$$)

Mass of the helium nucleus $$=4.001265 amu$$

Mass of proton $$=1.007277 amu$$

Mass of neutron $$=1.00866 amu$$

(take $$1 amu=931.4813 MeV)$$

$$M(^{40}Ca)=39.062591 u$$

$$M(^{39}Ca)=38.970719 u$$

$$M(^{40}Ca)=39.962383 u$$

$$M(^{39}Ar)=38.964314 u$$

$$m_n=1.008665 u$$

$$m(^{26}_{13}Al)\, =\, 25.986895\, u$$

$$m(^{27}_{13}Al)\, =\, 26.981541\, u$$

$$^{11}_{6}C\, \rightarrow\, ^{11}_5B\, +\, e^+\, +\, \nu $$: $$T_{1/2}$$ $$= 20.3\ min$$

The maximum energy of the emitted positron is $$0.960\ MeV$$.

Given the mass values:

$$m\, (^{11}_{6}C)\, =\, 11.011434\, u$$ and $$m\, (^{11}_{6}B)\, =\, 11.009305\, u$$

Calculate $$Q$$ and compare it with the maximum energy of the positron emitted.

Find the Q-value and the kinetic energy of the emitted $$\alpha$$- Particle in the $$\alpha$$-decay of (a) $$^{220}_{86}Rn$$ and (b) $$^{226}_{88}Ra$$.

Given:

$$m\, (^{226}_{88}Ra)\, =\, 226.02540\, u$$,

$$m\, (^{222}_{86}Rn)\, =\, 222.01750\, u$$,

$$m\, (^{216}_{84}Po)\, =\, 216.00189\, u$$

$$m\, (^{226}_{88}Ra)\, =\, 226.02540\, u$$,

$$m\, (^{222}_{86}Rn)\, =\, 222.01750\, u$$,

$$m\, (^{216}_{84}Po)\, =\, 216.00189\, u$$

$$m(^{238}_{92}U) = 238.05079 u$$

$$m(^{140}_{58}Ce )\, =\,139.90543\, u$$

$$m(^{99}_{44}U) =98.90594 u$$.

$$^{223}_{88}Ra\, \rightarrow\, ^{209}_{82}Pb\, +\, ^{14}_6C$$

$$^{223}_{88}Ra\, \rightarrow\, ^{219}_{86}Rn\, +\, ^{4}_2He$$

Calculate the Q-values for these decays and determine that both are energetically allowed.

$$e^+\, +\, ^A_ZX\, \rightarrow\, ^A_{Z - 1}Y\, +\, v$$

Show that if $$\beta^+$$ emission is energetically allowed, electron capture is necessarily allowed but not vice versa.

$$n+^{ 12 }{ C }\quad \rightarrow {^{ 9 } Be+\alpha }$$

whose threshold $${ E }_{ th }=6.17\ MeV$$. Find the kinetic energy of the alpha particles outgoing at right angles to the direction of the incoming neutron.

[Take $$u=931.1\ MeV$$]

(a) Find the equation describing accumulation of radio nuclide $$A_2$$ with time.

(b) Find the time interval after which the activity of radio nuclide $$A_2$$ reaches its maximum value.

$$\triangle E = (M_{Z - 1, N} + M_{H} - M_{Z, N})C^{2}$$

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

$$_{1}^{2}H + _{1}^{2}H \rightarrow _{2}^{3}He + _{0}^{1}n$$

The masses of deuteron, helium and neutron are $$2.015u, 0.017u$$ and $$1.009u$$ respectively. If $$1\ kg$$ of deuteron completely undergoes fusion, then calculate free energy.

$$[1u = 9.31\ MeV/c^{2}]$$.

$$n+_{ 5 }^{ 10 }{ B }\rightarrow _{ 3 }^{ 7 }{ Li }+_{ 2 }^{ 4 }{ He }$$

is observed to occur even when very slow-moving neutrons $$({M}_{n}=1.0087a.m.u)$$ strike a boron atom at rest. For a particular reaction in which $${K}_{n}=0$$, the helium $$({M}_{He}=4.0026a.m.u)$$ is observed to have a speed of $$9.30\times {10}^{6}m{s}^{-1}$$. Determine (a) the kinetic energy of the lithium $$({M}_{Li}=7.0160a.m.u)$$ and (b) the $$Q$$ value of the reaction.

$$n+_{ 92 }^{ 235 }{ U }\rightarrow _{ 92 }^{ 235 }{ U }^{\ast}\rightarrow _{ 52 }^{ 134 }{ Te }+3n$$

if the neutron is thermal. A thermal neutron is in thermal equilibrium with its environment; it has an average kinetic energy given by $$(3/2)kT$$.

Given $$m(n)=1.0087a.m.u$$, $$M(_{ }^{ 235 }{ U })=235.0439a.m.u$$; $$M(^{ 99 }{ Zr })=98.916a.m.u$$;

$$M(_{ }^{ 134 }{ Te })=133.9115a.m.u$$

$$M(_{ }^{ 134 }{ Te })=133.9115a.m.u$$

$$p+_{ }^{ 15 }{ N }\rightarrow _{ Z }^{ A }{ X }+n$$

(a) Find $$A,Z$$ and identify the nucleus $$X$$

(b) Find the $$Q$$ value of the reaction

(c) If the proton were to collide with the $$_{ }^{ 15 }{ N }$$ at rest, find the minimum KE needed by the proton to initiate the above reaction.

(d) If the proton has twice the energy in (c) and the outgoing neutron emerges at an angle of $${90}^{o}$$ with the direction of the incident proton, find the momentum of the nucleus $$X$$

[Given, $$m(p)=1.007825u,m(_{ }^{ 15 }{ C })=15.0106u$$

$$m(_{ }^{ 16 }{ N })=16.0061u,m(_{ }^{ 15 }{ N })=15.000u$$

$$m(_{ }^{ 16 }{ O })=15.9949u,m(n)=1.008665u$$,

$$m(_{ }^{ 15 }{ O })=15.0031u\quad and\quad 1u=931.5MeV$$]

(b) How much energy,in joules,is released by the complete fissioning of $$1.0 \ kg$$ of $$^{235}U$$? Assume $$Q = 200 \ MeV$$.

(c) For how long would this energy light a $$100 \ W$$ lamp?

$$^{52}Cr$$ | $$51.94051 \ u$$ | ^{26}Mg | $$25.98259 \ u$$ |

$$ ^2 H_1 + ^1 H_1 \rightarrow ^3 He_2 + photon $$

Here are some atomic masses.

$$^2 H_1$$ | $$2.014 102 \ u$$ |

$$^1 H_1$$ | $$1.007 825 \ u$$ |

$$^3 He_2$$ | $$3.016 029 \ u$$ |

g$$ of silicon so that the number density of conduction electrons in the silicon is increased by a multiply factor of $$10^6$$ from the $$10^{16} m^3$$ in pure silicon.

$$223{Ra} \rightarrow 209{pb} + 14C and 223{Ra} \rightarrow 219{Rn} + 4{He} $$

Calculate the Q value for the (a) first and (b) second decay and determine that both are energetically possible. (c) The Coulomb barrier height for alpha-particle emission is 30.0 MeV. What is the barrier height for $$^{14} C$$ emission? (Be careful about the nuclear radii.) The needed atomic masses are

$$^{223}Ra$$ 223.018 50 u $$^{14}C$$ 14.003 24 u

$$^{209}Pb$$ 208.981 07 u $$^4He$$ 4.002 60 u

$$^{219}Rn$$ 219.009 48 u

$$^2H + \ ^2H \rightarrow \ ^3He + n$$ $$ (Q=+3.27 \ MeV) $$,

$$^2H + \ ^2H \rightarrow \ ^3H + \ ^1H$$ $$ (Q=+4.03 \ MeV) $$, and

$$^2H + \ ^3H \rightarrow \ ^4He + n$$ $$ (Q=+17.59 \ MeV) $$,

The needed masses are

$$^1H$$ | $$1.007825 \ u$$ | $$^4He$$ | $$4.002603 \ u$$ |

$$^2H$$ | $$2.014102 \ u$$ | $$n$$ | $$1.008665 \ u$$ |

$$^3H$$ | $$3.016049 \ u$$ |

$$5 \ ^2H \rightarrow ^3He + ^4H + ^1H + 2n$$

(a) Calculate $$Q$$ for the fusion reaction. The following table is given for needed atomic masses.

$$^1H$$ | $$1.007 825 \ u$$ | $$^4He$$ | $$4.002 603 \ u$$ |

$$^2H$$ | $$2.014 102 \ u$$ | $$e^{\pm}$$ | $$0.000 548 6 \ u$$ |

$$^3He$$ | $$3.016 029 \ u$$ |

$$ ^{12}C + ^1H \rightarrow ^{13}N + \gamma $$ $$Q_1 = 1.95 \ MeV$$,

$$ ^{1}N \rightarrow ^{13}C + e^+ + v $$ $$Q_2 = 1.19$$,

$$ ^{13}C + ^1H \rightarrow ^{14}N + \gamma $$ $$Q_3 = 7.55$$,

$$ ^{14}N + ^1H \rightarrow ^{15}O + \gamma $$ $$Q_4 = 7.30$$,

$$ ^{15}O \rightarrow ^{15}N + e^+ + v $$ $$Q5 = 1.73$$, $$ ^{15}N + ^1H \rightarrow ^{12}C + ^4He $$ $$Q_6 = 4.97$$.

(a) Show that this cycle is exactly equivalent in its overall effects to the proton-proton cycle of the above figure. (b) Verify that the two cycles,as expected,have the same $$Q$$ value.

(i) Verify this by calculting the proton separation energy $${S}_{p}$$ for $${ _{ 50 }^{ }{ Sn } }^{ 120 }\left( Z=50 \right) $$ and $${ _{ 51 }^{ }{ Sb } }^{ 121 }\left( Z=51 \right) $$. The protn separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by

$${S}_{p}=[M{Z}_{-1,n}+{M}_{{H}^{-}}-{M}_{ZN}]{c}^{2}$$

Given $$_{ }^{ 119 }{ In }=118.9058u,_{ }^{ 120 }{ Sn }=119.902199u,_{ }^{ 121 }{ Sb }=120.903842u,_{ }^{ 1 }{ H }=1.0078252u$$

(ii) What does the existence of magic number indicate?

(a) Calculate the disintegration energy. What is the kinetic energy of (b) the proton and (c) the pion?

(a) $$\pi^{+} + p \rightarrow \sum^{+} + K^{+}$$ and (b) $$K^{-} + p \rightarrow \Lambda^{o} + \pi^{o}$$.

Given

$$m\left( _{ 88 }^{ 226 }{ Ra } \right) =226.02540u;\quad m\left( _{ 86 }^{ 222 }{ Rn } \right) =222.01750u;\quad m\left( _{ 86 }^{ 222 }{ Rn } \right) =220.01137u;\quad m\left( _{ 84 }^{ 216 }{ Po } \right) =216.00189u$$

(i) $$_{ 1 }^{ 1 }{ H }+_{ 1 }^{ 3 }{ H }\rightarrow _{ 1 }^{ 2 }{ H }+_{ 1 }^{ 2 }{ H }$$

(ii) $$_{ 6 }^{ 12 }{ C }+_{ 6 }^{ 12 }{ C }\rightarrow _{ 10 }^{ 20 }{ Ne }+_{ 2 }^{ 4 }{ He }$$

Atomic masses are given to be

$$m\left( _{ 1 }^{ 2 }{ H } \right) =2.014102u;\quad m\left( _{ 1 }^{ 3 }{ H } \right) =3.016049;\quad m\left( _{ 6 }^{ 12 }{ C } \right) =12.00000u;\quad m\left( _{ 10 }^{ 20 }{ Ne } \right) =19.992439u$$

$$\quad _{ 88 }^{ 223 }{ Ra }\rightarrow _{ 82 }^{ 209 }{ Pb }+_{ 6 }^{ 14 }{ C }$$

$$\quad _{ 88 }^{ 223 }{ Ra }\rightarrow _{ 86 }^{ 219 }{ Rn }+_{ 2 }^{ 4 }{ He }$$

Calculate the Q-values for these decays and determine that both are energetically allowed.

$$m\left( _{ 20 }^{ 40 }{ Ca } \right) =39.962591u;\quad m\left( _{ 20 }^{ 41 }{ Ca } \right) =40.962278u;\quad m\left( _{ 13 }^{ 26 }{ Al } \right) =25.986895u;\quad m\left( _{ 13 }^{ 27 }{ Al } \right) =26.981541u$$

(a) between the binding energies of their electrons in the ground state;

(b) between the wavelengths of first lines of the Lyman series.

(a) $$Li^{7} (p , n) Be^{7}$$;

(b) $$Be^{9} (n , \gamma ) Be^{10}$$;

(c) $$Li^{7} (\alpha , n ) B^{10} $$;

(d) $$O^{16} (d , \alpha) N^{14} $$

(a) a $$Li^{8}$$ atom whose nucleus has the binding energy $$41.3\,MeV$$;

(b) a $$C^{10}$$ nucleus whose binding energy per nucleon is equal to $$6.04\,MeV$$.

(a) the mean binding energy per one nucleon in $$O^{16}$$ nucleus;

(b) the binding energy of a neutron and an alpha-particle in a $$B^{11} $$ nucleus.

(c) the energy required for separation of an $$O^{16}$$ nucleus into four identical particles.

(a) the energy liberated in the fission of one kilogram of $$U^{235}$$ isotope, and the mass of coal with calorific value of $$30\,kJ/g$$ which is equivalent to that for one kg of $$U^{235}$$;

(b) the mass of $$U^{235}$$ isotope split during the explosion of the atomic bomb with $$30\,kt$$ trotyl equivalent if the calorific value of trotyl is $$4.1\,kJ/g$$.

$$p+ \ ^{15}N\rightarrow \ _Z^AX+n$$

a) Find $$A, Z$$ and identify the nucleus $$X$$.

b) Find the $$Q$$ value of the reaction.

c) If the proton were to collide with the $$^{15}N$$ at rest, find the minimum $$KE$$ needed by the proton to initiate the above reaction

- Alternating Current Extra Questions
- Atoms Extra Questions
- Current Electricity Extra Questions
- Dual Nature Of Radiation And Matter Extra Questions
- Electric Charges And Fields Extra Questions
- Electromagnetic Induction Extra Questions
- Electromagnetic Waves Extra Questions
- Electrostatic Potential And Capacitance Extra Questions
- Magnetism And Matter Extra Questions
- Moving Charges And Magnetism Extra Questions
- Nuclei Extra Questions
- Ray Optics And Optical Instruments Extra Questions
- Semiconductor Electronics: Materials, Devices And Simple Circuits Extra Questions
- Wave Optics Extra Questions