For a nucleus having mass number A and atomic number Z A. The surface energy per nucleon [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
For a nucleus ${}_{Z}^{A}X$ having mass number A and atomic number Z

A. The surface energy per nucleon $(b_{s}) = - a_{1} A^{2 / 3}$

B. The Coulomb contribution to the binding energy $b_{c} = - a_{2} \frac{Z (Z - 1)}{A^{4 / 3}}$

C. The volume energy $b_{v} = a_{3} A$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $a_{1}, a_{2}$ and $a_{3}$ are constants)

Choose the most appropriate answer from the options given below: [2023]

1 B, C, E only

2 C, D only

3 A, B, C, D only

4 B, C only

Ans.
(2)

$Surface energy per nucleon \propto \frac{r^{2}}{A} \propto \frac{A^{2 / 3}}{A} \propto \frac{1}{A^{1 / 3}}$
$(Mass number A \propto r^{3} \Rightarrow r \propto A^{1 / 3})$

$A is incorrect$

$Contribution to binding energy by coulombic forces is$

$= \frac{- a_{2} Z (Z - 1)}{A^{1 / 3}}$

$B is incorrect$

$Volume energy \propto A$

$C is correct$

$For (D), if we consider only surface energy contribution then option is correct.$

$For (E) only 3 interactions contribute to surface energy.$

Want Us to Email you About Special Offers & Updates?