MEDIUM

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Gold Nucleus $({}_{79}{Au}^{198})$ can decay into mercury nucleus $({}_{80}{Hg}^{198})$ by two decay schemes shown in figure. (i) It can emit a $β$ particle $(β_{1})$ and come to ground state by either emitting one $γ$ ray $(γ_{1})$ or emitting two $γ$ rays $(γ_{3} & γ_{2})$ (ii) It can emit one $x$ particle $(β_{2})$ and come to ground state by emitting $γ_{2}$ ray. Atomic masses: ${}^{198}{Au} = 197.9682 amu, {}^{198}{Hg} = 197.9662 amu, 1 amu = 930 MeV / c^{2} .$ The energy levels of the nucleus are shown in figure.

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Important Questions on Atoms and Nuclei

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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 :

HARD

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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:

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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}

)

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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>Atoms and Nuclei>Binding Energy and Its Calculation

Arrange $α, β, γ -$ rays in ascending order of their penetrating power.

HARD

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

Suppose a

{}_{88}^{226}{R a}

nucleus at rest and in ground state undergoes

α

-decay to a

{}_{86}^{222}{R n}

nucleus in its excited state. The kinetic energy of the emitted

α

particle is found to be

4.44 M e V . {}_{86}^{222}R n

nucleus then goes to its ground state by

γ

-decay. The energy of the emitted

γ

-photon is _______

k e V,

[Given: atomic mass of

_{88}^{226} R a = 226.005 u,

atomic mass of

_{86}^{222} R n = 222.000 u,

atomic mass of

α

particle

= 4.000 u, 1 u = 931 M e V / c^{2}, c

is speed of the light]

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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

)

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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 $1 u = 931.5 MeV$ )

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

Compare the charge and ionising power of $α and γ$ rays. Mention one use of radioactivity.

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

In gamma-decay, the number of nucleons in an unstable nucleus

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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}

]

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

In a gamma ray emission from nucleus

:

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

The energy equivalent of

0.5 g

of a substance is:

HARD

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

A fission reaction is given by

{}_{92}^{236}U \to {}_{54}^{140}{X e} + {}_{38}^{94}{S r} + 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_{X e}, K_{S r}, K_{x} (2 M e V)

and

K_{y} (2 M e V)

, respectively. Let the binding energies per nucleon of

{}_{92}^{236}U, {}_{54}^{140}{X e}

and

{}_{38}^{94}{S r}

7.5 MeV

8.5 MeV

, and

8.5 MeV

respectively. Considering different conservation laws, the correct option(s) is (are)

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

The energy required to break one bond in DNA is

10^{- 20} J

. This value in

eV

is nearly

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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}

MEDIUM

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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}

)

HARD

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

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)

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

What is radioactivity? State the law of radioactive decay.

EASY

Physics>Modern Physics>Atoms and Nuclei>Binding Energy and Its Calculation

What happens to the mass number and atomic number of an element when it emits

γ

-radiation

Important Questions on Atoms and Nuclei

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