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Introduction to Imperfections in Solids

Mp denotes th...

Question

$M_{p}$ denotes the mass of a proton and $M_{n}$ that of a neutron. A given nucleus, of binding energy $B$ , contains $Z$ protons and $N$ neutrons. The mass $M (N, Z)$ of the nucleus is given by
$(c is the velocity of light)$

A

M (N, Z) = N M_{n} + Z M_{p} + B / c^{2}

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B

M (N, Z) = N M_{n} + Z M_{p} - B c^{2}

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C

M (N, Z) = N M_{n} + Z M_{p} + B / c^{2}

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D

M (N, Z) = N M_{n} + Z M_{p} - B / c^{2}

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Solution

The correct option is D $M (N, Z) = N M_{n} + Z M_{p} - B / c^{2}$
Mass defect $Δ m = \frac{B}{c^{2}}$

Also,

Mass defect = Total Mass of protons + Total Mass of neutrons - Mass of the nucleus

$\Rightarrow$ Mass of the nucleus = Total Mass of protons + Total Mass of neutrons - Mass defect.

$\Rightarrow M (N, Z) = N M_{n} + Z M_{p} - \frac{B}{c^{2}}$

Hence, the option $(D)$ is correct.

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Similar questions

M_{p}

denotes the mass of a proton and

M_{n}

that of a neutron. A given nucleus, of binding energy

B

Z

N

neutrons. The mass

M (N, Z)

of the nucleus is given by (

C

is velocity of light):

_{Z}^{A} X

has mass represented by

M (A, Z)

M_{p}

M_{n}

denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then:

M_{p}

M_{n}

denote the masses of the nucleus, proton and neutron respectively in units of

u (1 u = 931.5 M e V / c^{2})

and BE represents its binding energy in MeV, then.

Q. Nuclear binding energy is the energy released during the hypothetical formation of the nucleus by the condensation of individual nucleons. Thus, binding energy per nucleon =

\frac{Total binding energy}{Number of nucleons}

For example, the mass of hydrogen atom is equal to the sum of the masses of a proton and an electron. For other atoms, the atomic mass is less than the sum of the masses of protons, neutrons and electrons present. This difference in mass, termed as mass defect, is a measure of the binding energy of protons and neutrons in the nucleus. The mass-energy relationship postulated by Einstein is expressed as:

Δ E = Δ m c^{2}

Δ E

is the energy liberated,

Δ m

is the loss of mass, and c is the speed of light.

M P

M n

are masses of a proton and a neutron respectively. For a nucleus, its binding energy is

B

and it contains

Z

N

neutrons, the correct relation for this nucleus if

C

is velocity of light is:

_{Z}^{A} X

has mass represented by

m (A, Z)

m_{p}

m_{n}

denote the mass of proton and neutron respectively and BE the binding energy(in MeV) then.

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