Chapter 42: Q 3 Exercise (page 1236)

Calculate the nuclear diameters of $(a) {}^{4}{He}, (b) {}^{56}{Fe}, and(c) {}^{238}U$ .

Short Answer

Expert verified

Therefore, the nuclear radius and diameters are:

$a.) r = 1.904 fm, d = 3.8097 fm b.) r = 4.59103 fm, d = 9.18206 fm c.) r = 7.43658 fm, d = 14.87317 fm$

Step by step solution

Given information

$r_{o} = 1.2 fm$

For radius we have,

$r = r_{o} A^{1 / 3}$

For diameter we have,

$d = 2 \cdot r$

Explanation

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

The radius is:

$r = r_{o} A^{1 / 3} r = (1.2 fm) (4)^{1 / 3} r = (1.2 fm) (1.587) r = 1.904 fm$

The diameter is:

$d = 2 \cdot r d = 2 \cdot 1.904 fm d = 3.8097 fm$

(b)The radius and diameter of the nucleus of ${}^{56}{Fe}$ must be determined:

The radius is:

$r = r_{o} A^{1 / 3} r = (1.2 fm) (56)^{1 / 3} r = (1.2 fm) (3.82586) r = 4.59103 fm$

The diameter is:

$d = 2 r d = 2 \times 4.59103 fm d = 9.18206 fm$

Explanation

(c)The radius and diameter of the nucleus of ${}^{238}U$ must be determined:

The radius is:

r = r_{o} A^{1 / 3} r = (1.2 fm) (238)^{1 / 3} r = (1.2 fm) (6.19715) r = 7.43658 fm

The diameter is:

$d = 2 r d = 2 \times 7.43658 fm d = 14.87317 fm$

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Calculate the nuclear diameters of $(a) {}^{4}{He}, (b) {}^{56}{Fe}, and(c) {}^{238}U$ .

Short Answer

Step by step solution

Given information

Explanation

Explanation

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

Short Answer

Step by step solution

Given information

Explanation

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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Calculate the nuclear diameters of $(a) {}^{4}{He}, (b) {}^{56}{Fe}, and(c) {}^{238}U$ .