EASY

Earn 100

For a nucleus ${}_{Z}^{A}X$ having mass number A and atomic number $Z$

A. The surface energy per nucleon $(b_{s}) = - a_{1} A^{\frac{2}{3}} .$

B. The Coulomb contribution to the binding energy $b_{c} = - a_{2} \frac{Z (Z - 1)}{A^{\frac{4}{3}}}$ .

C. The volume energy $b_{v} = a_{3} A$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $a_{1}, a_{2}$ and $a_{3}$ are constants)

Choose the most appropriate answer from the options given below:

47.83% studentsanswered this correctly

Important Questions on Nuclei

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

The energy required to break one bond in DNA is

10^{- 20} J

. This value in

eV

is nearly

MEDIUM

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

Find the Binding energy per nucleon for

{}_{50}^{120}{Sn}

. Mass of proton

m_{p} = 1.00783 u

, mass of neutron

m_{n} = 1.00867 u

and mass of tin nucleus

m_{Sn} = 119.902199 u

. (take

1 u = 931 MeV

)

MEDIUM

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

The energy equivalent of

0.5 g

of a substance is:

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

If the binding energy of

N^{14}

7.5 MeV

per nucleon and that of

N^{15}

7.7 MeV

per nucleon, then the energy required to remove a neutron from

N^{15}

HARD

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

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

\frac{e^{2}}{(4 π ϵ_{0})} = 1.44 MeV fm

. Assuming that the difference between the binding energies of

{}_{7}^{15}N a n d {}_{8}^{15}O

is purely due to the electrostatic energy, the radius of either of the nuclei is

(1 fm = 10^{- 15} m)

MEDIUM

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

In a process, certain amount of mass gets converted into energy. Let all the energy so converted be in the form of photons. If

700 \times 10^{12} Hz

is the mean frequency of the photons and if there are approximately

10^{30}

photons, what is the approximate mass that is converted into photons? (Assume

h = 6.6 \times 10^{- 34} J s, c = 3 \times 10^{8} m s^{- 1}

)

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

You are given that Mass of

{}_{3}^{7}{Li} = 7.0160 u,

Mass of

{}_{2}^{4}{He} = 4.0026 u

and Mass of

{}_{1}^{1}{He} = 1.0079 u

. When

20 g

{}_{3}^{7}{Li}

is converted into

_{2}^{4} He

by proton capture, the energy liberated, (in

kWh

), is: [Mass of nucleon

= 1 GeV / c^{2}

]

MEDIUM

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

The energy equivalent to a substance of mass $1 g$ is

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

Imagine that a reactor converts all the given mass into energy and that it operates at a power level of

10^{9} Watt

. The mass of the fuel consumed

per hour

, in the reactor, will be:
(velocity of light,

c

3 \times 10^{8} m s^{- 1}

)

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

The binding energy per nucleon of

{}_{5} B^{10}

8.0 MeV

and that of

{}_{5} B^{11}

7.5 MeV .

The Energy required to remove a neutron from

{}_{5} B^{11}

is (mass of electron and proton are

9.11 \times 10^{- 31} kg

and

1.67 \times 10^{- 27} kg

)

MEDIUM

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

A nucleus

X

emits a

β

-particle to produce a nucleus

Y

. If their atomic masses are

M_{x}

and

M_{y}

respectively, then the maximum energy of the

β

-particle emitted is (where,

m_{e}

is the mass of an electron and

c

is the velocity of light)

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

A particle of rest mass

m_{0}

is travelling, so that its total energy is twice its rest mass energy. It collides with another stationary particle of rest mass

m_{0}

to form a new particle. What is the rest mass of the new particle?

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

The mass-defect in a nuclear fusion reaction is

0.3

per cent. The amount of energy released in one

kg

of fusion reaction is

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

What is the binding energy of ${}_{14}^{29}S i$ whose atomic mass is $28.976495 u$

Mass of proton $= 1.007276 u$

Mass of neutron $= 1.008664 u$

(Neglect the electron mass) (Assume $1 u = 931.5 MeV$ )

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

In a certain mass spectrometer, an ion beam passes through a velocity filter consisting of mutually perpendicular fields E and B. The beam then enters a region of another magnetic field

B^{'}

, perpendicular to the beam. The radius of curvature of the resulting ion beam is proportional to

MEDIUM

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

Find the energy equivalent of one atomic mass unit in Joules and in

MeV .

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

The binding energy of a nucleus is equivalent to

EASY

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

If the binding energy of the electron in a hydrogen atom is

13.6 eV

, the energy required to remove the electron from the first excited state of

{Li}^{+ +}

is :

MEDIUM

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

Two deuterons undergo nuclear fusion to form a Helium nucleus. The energy released in this process is (given binding energy per nucleon for deuteron

= 1.1 MeV

and for helium

= 7.0 MeV

)

HARD

Physics>Modern Physics>Nuclei>Mass-Energy and Nuclear Binding Energy

Consider the nuclear fission,

{Ne}^{20} \to 2 {He}^{4} + C^{12}

. Given that the binding energy/nucleon of

{Ne}^{20}, {He}^{4}

and

C^{12}

are

8.03 MeV, 7.86 MeV

, respectively. Identify the correct statement:

Important Questions on Nuclei

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