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Reasons of Stability

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Question

Calculate the minimum energy needed to separate a neutron from nucleus with Z protons and N neutrons in terms of the masses $M_{Z, N}, M_{Z, N - 1}$ and the mass of the neutron,

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Solution

$E_{2} N = E_{Z, N - 1} +_{0}^{1} n$
energy released = (initial mas of nucleus - final mass of nucleus $) c^{2} = (M_{Z n - 1 + M_{g} + M_{Z n}}) c^{2}$

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Q. Show that the minimum energy needed to separate a proton from a nucleus with Z protons and N neutrons is

∆ E = (M_{Z - 1, N} + M_{B} - M_{Z, N}) c^{2}

where M_Z_,N = mass of an atom with Z protons and N neutrons in the nucleus and M_B = mass of a hydrogen atom. This energy is known as proton-separation energy.

Show that the minimum energy needed to separate a proton from a nucleus with Z protons and N neutrons is $△ E = (M_{z - 1, N} + M_{H} - M_{Z, n}) C^{2}$ 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.

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)

M, M

_{n}

M

_{p}

denotes the masses of a nucleus of

_{Z} X^{A}

, a neutron, and a proton respectively. If the nucleus is separated into its individual protons and neutrons 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:

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