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morpeh [17]
2 years ago
7

Determine the nuclear radius (in fm) for each of the following nuclei.

Physics
1 answer:
tekilochka [14]2 years ago
4 0

Answer:

(a) 2.75 fm

(b) 2.89 fm

(c) 4.70 fm

(d) 7.12 fm

Explanation:

For a given element, the radius r of its nuclei is given by;

r = r₀A^{(1/3)}

Where;

A = Atomic mass of the element

r₀ = 1.2 x 10⁻¹⁵m = 1.2fm

Now let's solve for the given elements

(a) ¹²₆C

Carbon element => This has an atomic mass number of 12

Therefore its radius is given by;

r = 1.2  x 12^{1/3}

r = 1.2 x 2.29

r = 2.75 fm

(b) ¹⁴₇N

Nitrogen element => This has an atomic mass number of 14

Therefore its radius is given by;

r = 1.2  x 14^{1/3}

r = 1.2 x 2.41

r = 2.89 fm

(c) ⁶⁰₂₇Co

Cobalt element => This has an atomic mass number of 60

Therefore its radius is given by;

r = 1.2  x 60^{1/3}

r = 1.2 x 3.92

r = 4.70 fm

(d) ²⁰⁸₈₂Pb

Lead element => This has an atomic mass number of 208

Therefore its radius is given by;

r = 1.2  x 208^{1/3}

r = 1.2 x 5.93

r = 7.12 fm

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