Question

Unreasonable Results

A physicist scatters\(\gamma \)rays from a substance and sees evidence of a nucleus\(7.5 \times {10^{ - 13}}\;{\rm{m}}\)in radius. (a) Find the atomic mass of such a nucleus.

(b) What is unreasonable about this result?

(c) What is unreasonable about the assumption?

Short answer

a) The atomic mass of a nucleus is \(2.4 \times {10^8}\,{\rm{u}}\).

b) The result is irrational because the atomic mass value is extremely high.

c) The nucleus has a large radius.

Step-by-step solution

Definition of atomic mass

The mass of a single atom in a chemical element is known as its atomic mass.

The size of an atom is determined by its atomic mass.

Find the atomic mass

a)

Let us solve the given problem.

The formula for the relationship between proton radius, nucleus radius, and atomic mass is:

\(\begin{aligned}{}r = {r_0}{A^{\frac{1}{3}}}\\A = {\left( {\frac{r}{{{r_0}}}} \right)^3}\end{aligned}\)

Where \({r_0} = \) radius of proton, \(r = \)radius of nucleus and \(A = \)atomic mass

Now plug in the value of \(r,\,\,{r_0}\)in the above equation and solve for the value of \(A\)

\(\begin{aligned}{}A = \left( {\frac{{7.5 \times {{10}^{ - 13}}\;{\rm{m}}}}{{1.2 \times {{10}^{ - 15}}\;{\rm{m}}}}} \right)\\ = 2.4 \times {10^8}{\rm{u}}A\\ = 2.4 \times {10^8}{\rm{u}}\end{aligned}\)

Therefore, value of \(A\)is \(2.4 \times {10^8}{\rm{u}}\).

Unreasonable about result in part a)

b)

The unreasonable about the result is that the value of atomic mass is vey high.

 Unreasonable about assumption in part a)

c)

The radius of nucleus is very high.