# The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei ""_20^41"Ca" and ""_13^27 "Al" - Physics

Numerical

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei ""_20^41"Ca" and ""_13^27 "Al" from the following data:

"m"(""_20^40"Ca") = 39.962591 u

"m"(""_20^41"Ca") = 40.962278 u

"m"(""_13^26"Al") = 25.986895 u

"m"(""_13^27"Al") = 26.981541 u

#### Solution

For ""_20^41"Ca": Separation energy  = 8.363007 MeV

For ""_13^27"Al": Separation energy = 13.059 MeV

A neutron (""_0"n"^1) is removed from a ""_20^41 "Ca" nucleus. The corresponding nuclear reaction can be written as:

""_20^41"Ca" -> ""_20^40"Ca" + _0^1"n"

It is given that:

Mass "m"(""_20^40 "Ca")= 39.962591 u

Mass "m"(""_20^41 "Ca") = 40.962278 u

Mass m(""_0"n"^1) = 1.008665 u

The mass defect of this reaction is given as:

Δ m = "m"(""_20^40"Ca") + (""_0^1"n") - "m"(""_20^41 "Ca")

= 39.962591 + 1.008665 - 40.962278 = 0.008978 "u"

But 1 u = 931.5 MeV/c2

∴ Δ m = 0.008978 × 931.5 MeV/c2

Hence, the energy required for neutron removal is calculated as:

"E" = triangle"mc"^2

= 0.008978 xx 931.5 = 8.363007 MeV

For ""_13^27 "Al" the neutron removal reaction can be written as:

$\ce{^27_13Al -> ^26_13Al + ^1_0n}$

it us given that.

Mass "m"(""_13^27 "Al") = 26.981541 u

Mass "m"(""_13^26 "Al") = 25.986895 u

The mass defect of this reaction is given as:

triangle"m" = "m"(""13^26 "Al") + "m"(""_0^1 "n") - "m"(""_13^27 "Al")

= 25.986895 + 1.008665 - 26.981541

= 0.014019 u

= 0.014019 xx 931.5 " MeV/c"^2

Hence, the energy required for neutron removal is calculated as:

E = triangle"mc"^2

= 0.014019 x 931.5 = 13.059 MeV

Concept: Mass-energy and Nuclear Binding Energy - Nuclear Binding Energy
Is there an error in this question or solution?

#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 13 Nuclei
Exercise | Q 13.24 | Page 464
NCERT Class 12 Physics Textbook
Chapter 13 Nuclei
Exercise | Q 24 | Page 464

Share