Nucleus and Nuclear Reaction

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LEVELJEE Main

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

first increase then decrease

LEVELJEE Main

If a star can convert all the He nuclei completely into oxygen nuclei. The energy released per oxygen nuclei is : (Mass of the helium nucleus is $4.0026 amu$ and mass of oxygen nucleus is $15.9994 amu$ )

(A)

7.6 MeV

(B)

56.12 MeV

(C)

10.24 MeV

(D)

23.4 MeV

LEVELJEE Main

Consider the reaction : $_{1}^{2} H +_{1}^{2} H =_{2}^{4} He + Q$ . Mass of the deuterium atom = 2.0141 u. Mass of helium atom = 4.0024 u. This is a nuclear ........ reaction in which the energy $Q$ released is ...... MeV.

JEE Advanced 2009

LEVELJEE Advanced

Comprehension Passage

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen,

_{1}^{2} H

known as deuteron and denoted by D can be thought of as a candidate for fusion reactor. The D-D reaction is

_{1}^{2} H +_{1}^{2} H \to_{2}^{3} He + n + energy

. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of

_{1}^{2} H

nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time

t_{0}

before the particles fly away from the core. If

n

is the density (number/volume) of deuterons, the product

n t_{0}

is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than

5 \times 1 0^{14} s cm^{- 3}

. It may be helpful to use the following : Boltzmann constant

k = 8.6 \times 1 0^{- 5} eV/K

;

\frac{e ^{2}}{4 π ε _{0}} = 1.44 \times 1 0^{- 9} eVm

Question 1:

In the core of nuclear fusion reactor, the gas becomes plasma because of

(A)

strong nuclear force acting between the deuterons.

(B)

Coulomb force acting between the deuterons.

(C)

Coulomb force acting between deuteron-electron pairs.

(D)

the high temperature maintained inside the reactor core.

Question 2:

Assume that two deuteron nuclei in the core of fusion reactor at temperature $T$ are moving towards each other, each with kinetic energy $1.5 k T$ , when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature $T$ required for them to reach a separation of $4 \times 1 0^{- 15} m$ is in the range

(A)

1.0 \times 1 0^{9} K < T < 2.0 \times 1 0^{9} K

(B)

2.0 \times 1 0^{9} K < T < 3.0 \times 1 0^{9} K

(C)

3.0 \times 1 0^{9} K < T < 4.0 \times 1 0^{9} K

(D)

4.0 \times 1 0^{9} K < T < 5.0 \times 1 0^{9} K

Question 3:

Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion ?

(A)

Deuteron density

= 2.0 \times 1 0^{12} cm^{- 3}

, confinement time

= 5.0 \times 1 0^{- 3} s

(B)

Deuteron density

= 8.0 \times 1 0^{14} cm^{- 3}

, confinement time

= 9.0 \times 1 0^{- 1} s

(C)

Deuteron density

= 4.0 \times 1 0^{23} cm^{- 3}

, confinement time

= 1.0 \times 1 0^{- 11} s

(D)

Deuteron density

= 1.0 \times 1 0^{24} cm^{- 3}

, confinement time

= 4.0 \times 1 0^{- 12} s

LEVELBoard

The mass number of a nucleus is

* Multiple Correct Options

(A)

always less than its atomic number.

(B)

always more than its atomic number.

(C)

sometimes equal to its atomic number.

(D)

sometimes more than and sometimes equal to its atomic number.

JEE Advanced 2015

LEVELJEE Advanced

A fission reaction is given by $_{92}^{236} U \to_{54}^{140} Xe +_{38}^{94} Sr + x + y$ , where $x$ and $y$ are two particles. Considering $_{92}^{236} U$ to be at rest, the kinetic energies of the products are denoted by $K_{Xe}$ , $K_{Sr}$ , $K_{x}$ (2 MeV) and $K_{y}$ (2 MeV), respectively. Let the binding energies per nucleon of $_{92}^{236} U$ , $_{54}^{140} Xe$ and $_{38}^{94} Sr$ be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct options is/are

* Multiple Correct Options

(A)

x = n

y = n

K_{Sr} = 129 MeV

K_{Xe} = 86 MeV

(B)

x = p

y = e^{-}

K_{Sr} = 129 MeV

K_{Xe} = 86 MeV

(C)

x = p

y = n

K_{Sr} = 129 MeV

K_{Xe} = 86 MeV

(D)

x = n

y = n

K_{Sr} = 86 MeV

K_{Xe} = 129 MeV

LEVELBoard

How many electrons, protons and neutrons are there in a nucleus of atomic number $11$ and mass number $24$ ? Find, (a) Number of electrons. (b) Number of protons. (c) Number of neutrons.

LEVELJEE Main

Order of magnitude of density of uranium nucleus is ( $m_{p} = 1.67 \times 1 0^{- 27} kg$ )

(A)

1 0^{20} kg/m^{3}

(B)

1 0^{17} kg/m^{3}

(C)

1 0^{14} kg/m^{3}

(D)

1 0^{11} kg/m^{3}

LEVELJEE Main

Fast neutrons can easily be slowed down by

(A)

the use of lead shielding

(B)

passing them through heavy water

(C)

elastic collisions with heavy nuclei

(D)

applying a strong electric field

LEVELBoard

The equation; $4_{1}^{1} H ⟶_{2}^{4} He^{2 +} + 2 e^{-} + 26 MeV$ represents

(A)

β

-decay

(B)

γ

It is proposed to use the nuclear fusion reaction; $_{1}^{2} H +_{1}^{2} H \to_{2}^{4} He$ in a nuclear reactor of $200 MW$ rating. If the energy from the above reaction is used with a $25$ per cent efficiency in the reactor, how many grams of deuterium fuel will be needed per day? (The masses of $_{1}^{2} H$ and $_{2}^{4} He$ are $2.0141$ atomic mass units and $4.0026$ atomic mass units respectively.)

JEE Advanced 2001

LEVELJEE Main

In a nuclear reactor $^{235} U$ undergoes fission liberating $200 MeV$ of energy. The reactor has a $10%$ efficiency and produces $1000 MW$ power. If the reactor is to function for $10 yr$ , find the total mass of uranium required.

JEE Advanced 2016

LEVELJEE Advanced

The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by $E = \frac{3}{5} \frac{Z ( Z - 1 ) e ^{2}}{4 π ε _{0} R}$ The measured masses of the neutron, $_{1}^{1} H$ , $_{7}^{15} N$ and $_{8}^{15} O$ are $1.008665 u$ , $1.007825 u$ , $15.000109 u$ and $15.003065 u$ , respectively. Given that the radii of both the $_{7}^{15} N$ and $_{8}^{15} O$ nuclei are same, $1 u = 931.5 MeV/c^{2}$ ( $c$ is the speed of light) and $e^{2} / (4 π ε_{0}) = 1.44 MeV fm$ . Assuming that the difference between the binding energies of $_{7}^{15} N$ and $_{8}^{15} O$ is purely due to the electrostatic energy, the radius of either of the nuclei is ( $1 fm = 1 0^{- 15} m$ )

Binding energy per nucleon versus mass number curve for nuclei is shown in figure. $W$ , $X$ , $Y$ and $Z$ are four nuclei indicated on the curve. The process that would release energy is

(A)

Y \to 2 Z

(B)

W \to X + Z

(C)

W \to 2 Y

(D)

X \to Y + Z

LEVELJEE Main

From the following equations pick out the possible nuclear fusion reactions

* Multiple Correct Options

(A)

_{6} C^{13} +_{1} H^{1} ⟶_{6} C^{14} + 4.3 MeV

(B)

_{6} C^{12} +_{1} H^{1} ⟶_{7} N^{13} + 2 MeV

(C)

_{7} N^{14} +_{1} H^{1} ⟶_{8} O^{15} + 7.3 MeV

(D)

_{92} U^{235} +_{0} n^{1} ⟶_{54} Xe^{140} +_{36} Sr^{94} +_{0} n^{1} +_{0} n^{1} + γ + 200 MeV

LEVELBoard

For uranium nucleus how does its mass vary with volume ?

(A)

m \propto V

(B)

m \propto 1/ V

(C)

m \propto V

(D)

m \propto V^{2}

JEE Advanced 1986

LEVELBoard

Atoms having the same ...... but different ...... are called isotopes.

LEVELJEE Main

The binding energies per nucleon for deuteron ( $_{1} H^{2}$ ) and helium ( $_{2} He^{4}$ ) are $1.1 MeV$ and $7.0 MeV$ respectively. The energy released when two deuterons fuse to form a helium nucleus ( $_{2} He^{4}$ ) is ......... .

JEE Advanced 1986

LEVELBoard

When boron nucleus $(_{5}^{10} B)$ is bombarded by neutrons, $α$ -particles are emitted. The resulting nucleus is of the element ........... and has the mass number…… .

JEE Advanced 2015

LEVELJEE Main

Match the nuclear processes given in Column I with the appropriate option(s) in Column II.

List-I

(P)

Nuclear fusion

(Q)

Fission in a nuclear reactor

(R)

β

-decay

(S)

γ

-ray emission

List-II

(1)

absorption of thermal neutrons by

_{92}^{235} U

(2)

_{27}^{60} Co

nucleus

(3)

Energy production in stars via hydrogen conversion to helium

Let $m_{p}$ be the mass of proton, $m_{n}$ the mass of neutron. $M_{1}$ the mass of $_{10}^{20} Ne$ nucleus and $M_{2}$ the mass of $_{20}^{40} Ca$ nucleus. Then

* Multiple Correct Options

(A)

M_{2} = 2 M_{1}

(B)

M_{2} > 2 M_{1}

(C)

M_{2} < 2 M_{1}

(D)

M_{1} < 10 (m_{n} + m_{p})

LEVELJEE Advanced

A star initially has $1 0^{40}$ deuterons. It produces energy via the processes $_{1}^{2} H +_{1}^{2} H \to_{1}^{3} H + p$ and $_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He + n$ . If the average power radiated by the star is $1 0^{16}$ W, the deuteron supply of the star is exhausted in a time of the order of The mass of the nuclei are as follows: $M (H^{2}) = 2.014 amu$ ; $M (n) = 1.008 amu$ ; $M (p) = 1.007 amu$ ; $M (He^{4}) = 4.001 amu$ .

(A)

1 0^{6}

(B)

1 0^{8}

(C)

1 0^{12}

(D)

1 0^{16}

LEVELJEE Main

In the following, Column I lists some physical quantities and the Column II gives approximate energy values associated with some of them. Choose the appropriate value of energy from Column II for each of the physical quantities in Column I and write the corresponding letters A, B, C etc., against the number (i), (ii) and (iii) etc., of the physical quantity.

List-I

(P)

Energy of thermal neutrons

(Q)

Energy of X-ray

(R)

Binding energy per nucleon

(S)

Photoelectric threshold of a metal

List-II

Assume that the nuclear binding energy per nucleon $(B / A)$ versus mass number $(A)$ is as shown in the figure. Use this plot to choose the correct choice(s) given below.

* Multiple Correct Options

(A)

Fusion of two nuclei with mass numbers lying in the range of

1 < A < 50

will release energy.

(B)

Fusion of two nuclei with mass numbers lying in the range of

51 < A < 100

will release energy.

(C)

Fission of a nucleus lying in the mass range of

100 < A < 200

will release energy when broken into two equal fragments.

(D)

Fission of a nucleus lying in the mass range of

200 < A < 260

will release energy when broken into two equal fragments.

JEE Advanced 2013

LEVELJEE Advanced

Comprehension Passage

The mass of a nucleus

_{Z}^{A} X

is less than the sum of the masses of

(A - Z)

number of neutrons and

Z

number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass

M

can break into two light nuclei of masses

m_{1}

and

m_{2}

only if

(m_{1} + m_{2}) < M

. Also two light nuclei of masses

m_{3}

and

m_{4}

can undergo complete fusion and form a heavy nucleus of mass

M^{'}

only if

(m_{3} + m_{4}) > M^{'}

. The masses of some neutral atoms are given in the table below: $\begin{array}{llll} _{1}^{1}\text{H} & 1.007825\text{u} & _{1}^{2}\text{H} & 2.014102\text{u} \\ _{3}^{6}\text{Li} & 6.01513\text{u} & _{3}^{7}\text{Li} & 7.016004\text{u} \\ _{64}^{152}\text{Gd} & 151.919803\text{u} & _{82}^{206}\text{Pb} & 205.974455\text{u} \\ _{1}^{3}\text{H} & 3.016050\text{u} & _{2}^{4}\text{He} & 4.002603\text{u} \\ _{30}^{70}\text{Zn} & 69.925325\text{u} & _{34}^{82}\text{Se} & 81.916709\text{u} \\ _{84}^{210}\text{Po} & 209.982876\text{u} & & \end{array}$

Question 1:

The correct statement is

(A)

The nucleus

_{3}^{6} Li

can emit an alpha particle.

(B)

The nucleus

_{84}^{210} Po

can emit a proton.

(C)

Deuteron and alpha particle can undergo complete fusion.

(D)

The nuclei

_{30}^{70} Zn

and

_{34}^{82} Se

can undergo complete fusion.

Question 2:

The kinetic energy (in keV) of the alpha particle, when the nucleus $_{84}^{210} Po$ at rest undergoes alpha decay, is

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

Comprehension Passage

In the core of nuclear fusion reactor, the gas becomes plasma because of

Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion ?

The mass number of a nucleus is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Order of magnitude of density of uranium nucleus is (mp​=1.67×10−27 kg)

Fast neutrons can easily be slowed down by

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The equation; 4 11​H⟶ 24​He2++2e−+26 MeV represents

From the following equations pick out the possible nuclear fusion reactions

For uranium nucleus how does its mass vary with volume ?

Atoms having the same ...... but different ...... are called isotopes.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } When boron nucleus (510​B) is bombarded by neutrons, α-particles are emitted. The resulting nucleus is of the element ........... and has the mass number…… .

Match the nuclear processes given in Column I with the appropriate option(s) in Column II.

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let mp​ be the mass of proton, mn​ the mass of neutron. M1​ the mass of 1020​Ne nucleus and M2​ the mass of 2040​Ca nucleus. Then

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.

Comprehension Passage

The correct statement is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The kinetic energy (in keV) of the alpha particle, when the nucleus 84210​Po at rest undergoes alpha decay, is

Order of magnitude of density of uranium nucleus is ( $m_{p} = 1.67 \times 1 0^{- 27} kg$ )

The equation; $4_{1}^{1} H ⟶_{2}^{4} He^{2 +} + 2 e^{-} + 26 MeV$ represents

When boron nucleus $(_{5}^{10} B)$ is bombarded by neutrons, $α$ -particles are emitted. The resulting nucleus is of the element ........... and has the mass number…… .

Let $m_{p}$ be the mass of proton, $m_{n}$ the mass of neutron. $M_{1}$ the mass of $_{10}^{20} Ne$ nucleus and $M_{2}$ the mass of $_{20}^{40} Ca$ nucleus. Then

Assume that the nuclear binding energy per nucleon $(B / A)$ versus mass number $(A)$ is as shown in the figure. Use this plot to choose the correct choice(s) given below.

The kinetic energy (in keV) of the alpha particle, when the nucleus $_{84}^{210} Po$ at rest undergoes alpha decay, is