Name: Einstein's Mass - Energy Relation
Uploaded: 2019-07-19
Duration: 5 min 21 s
Description: Do you know that mass can also be converted into energy? Well, most of you won't agree but it's actually true. Let's watch the video and learn more.

Question

What do you understand by 'binding energy of a nucleus'? Derive binding energy equation for the nucleus of an atom

{}_{Z}X^{A}

in terms of atomic masses and neutrons mass. State the approximation involved and justify it.

Accepted Answer

The binding energy of a nucleus is defined as the minimum energy required to separate its nucleons and place them at rest at an infinite distance apart. Thus,

$BE$ = $(∆ m) c^{2} = [{Zm}_{p} + (A - Z) m_{n} - m_{N}] c^{2} . . . . . (1)$

The electron binding energy is, however, negligible compared to nucleon binding energy. Thus,

$m (_{Z} X^{A}) = m_{N} + {Zm}_{e} or m_{N} = m (_{Z} X^{A}) - {Zm}_{e} .$

Substituting this value of $m_{N}$ in Eq. (1), we get

$BE = [Z (m_{p} + m_{e}) + (A - Z) m_{n} - m (_{Z} X^{A})] c^{2} .$

But $m_{p} + m_{e} = m_{H},$ the mass of hydrogen atom which contains one proton and one electron. Thus

$BE = [{Zm}_{H} + (A - Z) m_{n} - m (_{Z} X^{A})] c^{2} . . . . . (2)$

This is the expression for the nuclear binding energy of an atom ${}_{Z}X^{A}$ in terms of atomic masses and neutron mass.

Eqs. (1) and (2) are identical, because in Eq. (2) masses of $Z$ electrons appearing in the first and the third term mutually cancel.

Since $1 u \times c^{2} = 931.5 MeV, the Eq . (2) can also be written as$

$BE = [{Zm}_{H} + (A - Z) m_{n} - m (_{Z} X^{A})] \times 931.5 MeV .$

The effect of electron binding energy is neglected as it has little effect on the nucleus.It is assumed that the binding energy of electrons is much smaller $(eV to keV)$ as compared to the rest mass od a nucleon $(10^{3} MeV)$

What do you understand by 'binding energy of a nucleus'? Derive binding energy equation for the nucleus of an atom ${}_{Z}X^{A}$ in terms of atomic masses and neutrons mass. State the approximation involved and justify it.

Important Questions on Mass-Energy Equivalence : Nuclear Binding Energy

Learn and Prepare for any exam you want !

What do you understand by 'binding energy of a nucleus'? Derive binding energy equation for the nucleus of an atom XAZ in terms of atomic masses and neutrons mass. State the approximation involved and justify it.

Important Questions on Mass-Energy Equivalence : Nuclear Binding Energy

Learn and Prepare for any exam you want !

What do you understand by 'binding energy of a nucleus'? Derive binding energy equation for the nucleus of an atom ${}_{Z}X^{A}$ in terms of atomic masses and neutrons mass. State the approximation involved and justify it.