Chapter 14, Problem 3MPS

To determine

To Find: The number of protons in the nitrogen atoms.

Answer to Problem 3MPS

The number of proton in one nitrogen atom is $7$ .

Explanation of Solution

Given:

The three oxygen and two nitrogen atoms contain 38 protons. Five oxygen atoms and three nitrogen atoms has 61 protons.

Calculation:

Consider $x$ is the number of proton in oxygen atom and $y$ is the number of proton in nitrogen atom.

Consider the equation formed by the given data is,

  $\begin{array}{l}3x+2y=38\\ 5x+3y=61\end{array}$

Then, rewrite the above equation as,

  $\begin{array}{l}-3\left(3x+2y\right)=38\left(-3\right)\\ \left(5x+3y\right)2=61\left(2\right)\end{array}$

Then,

  $\begin{array}{l}-9x-6y=-114\\ 10x+6y=122\end{array}$

Add both the equations as,

  $x=8$

Substitute $x=8$ in the equation $3x+2y=38$ as,

  $\begin{array}{l}3\left(8\right)+2y=38\\ 24+2y=38\\ y=7\end{array}$

Thus, the number of proton in one nitrogen atom is $7$ .