Chapter 10, Problem 10.1CYU

Check Your Understanding Nucleus X is two times larger than nucleus Y. What is the ratio of their atomic masses?

To determine

Ratio of atomic mass of nucleus X and nucleus Y.

Answer to Problem 10.1CYU

8:1.

Explanation of Solution

Given Information:

  $\text{Nucleus }X=\text{2}\times \text{Nucleus }Y$

Formula used:

Atomic mass and radius of the nucleus is given by,

  $r=r_0{A}^{\frac{1}{3}}.$ ...........................(1)

Where,

r = Radius of the nucleus

r₀ = Radius of a single proton

A = Atomic mass

Calculation:

For nucleus X:

Equation (1) becomes,

  $r_X=r_0{A}_X{}^{\frac{1}{3}}$

For nucleus Y:

Equation (1) becomes,

  $r_Y=r_0{A}_Y{}^{\frac{1}{3}}$

But,

  $\begin{array}{l}{r}_X=2r\\ r_Y=r\\ \\ r_X=r_0{A}_X{}^{\frac{1}{3}}\\ 2r=r_0{A}_X{}^{\frac{1}{3}}\\ 2(r_0{A}_Y{}^{\frac{1}{3}})=r_0{A}_X{}^{\frac{1}{3}}\\ 2=\frac{A_X{}^{\frac{1}{3}}}{A_Y{}^{\frac{1}{3}}}\\ {(}^{\frac{A_X}{A_Y}}=2\\ \frac{A_X}{A_Y}=2^3=8\\ \frac{\text{Atomic}\text{mass}\text{of}X}{\text{Atomic}\text{mass}\text{of}Y}=\frac{8}{1}\end{array}$

Conclusion:

In this way, the atomic mass of the nucleus can be determined by the relation between the radius of an atom and atomic mass of an atom.