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Modern Physics
Found in: Page 518
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

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Short Answer

a) For a nucleus of A=220, estimate very roughly how many nucleons would be at the surface.

b) If the binding energy of an interior nucleon due to the internucleon attraction were E1 and if all nucleon were are tightly bound, the total binding energy would be AE1 . Taking into account the different binding of surface nucleons, roughly what would be the total binding energy?

a) The number of nucleons at the surface of the nucleus is roughly 145.

b) The total binding energy of nucleus is approximate 150EI.

See the step by step solution

Step by Step Solution

Step 1: Given data

Atomic number of nucleus, A=220 .

Radius of nucleons, R0 is 1.2×1015 m.

Binding energy of interior nucleon is EI.

Binding energy of surface nucleon is EI/2.

Step 2: Formula of Area of nucleus

Area of the nucleus is given as:


Where, r is the radius of large sphere, Ro is the radius of nucleon.

Step 3: Calculation for the number of nucleon


The area contribution of each nucleon present on the boundary surface is πRo2 where, Ro=1.2×1015 m.

Surface area of the nucleus is given as:

anucleus =4πr2anucleus =4π(A1/3Ro)2anucleus =4πA2/3R2o


The number of nucleon present on the surface as shown below.

N=anucleus anucleusN=4π2/3R02πRo2

Substitute the values of area of nucleus in the above equation.

N=4A2/3N=4 2202/3N=145.77

Step 4: Calculation for the binding energy of nucleon


The total number of nucleons in the interior of the nucleus is 220145=75.

Binding energy of each interior nucleon is EI and each surface nucleon contributes about half as much binding energy, that is (El2) .

The total binding energy would be given as follows:

Binding energy =75EI+145(EI2)=147.5EI.

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