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Chapter 42: Q 3 Exercise (page 1236)

Calculate the nuclear diameters of(a)He4,(b)Fe56, and(c)U238.

Short Answer

Expert verified

Therefore, the nuclear radius and diameters are:

a.)r=1.904fm,d=3.8097fmb.)r=4.59103fm,d=9.18206fmc.)r=7.43658fm,d=14.87317fm

Step by step solution

01

Given information

ro=1.2fm

For radius we have,

r=roA1/3

For diameter we have,

d=2·r

02

Explanation

(a)The radius and diameter of the nucleus of 4He must be determined:

The radius is:

r=roA1/3r=(1.2fm)(4)1/3r=(1.2fm)(1.587)r=1.904fm

The diameter is:

d=2·rd=2·1.904fmd=3.8097fm

(b)The radius and diameter of the nucleus of Fe56must be determined:

The radius is:

r=roA1/3r=(1.2fm)(56)1/3r=(1.2fm)(3.82586)r=4.59103fm

The diameter is:

d=2rd=2×4.59103fmd=9.18206fm

03

Explanation

(c)The radius and diameter of the nucleus of U238must be determined:

The radius is:

r=roA1/3r=(1.2fm)(238)1/3r=(1.2fm)(6.19715)r=7.43658fm

The diameter is:

d=2rd=2×7.43658fmd=14.87317fm

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