Questions: Based on your answer in Part B, how many neutrons are in this amount of ^13C? Express your answer numerically in neutrons.

Solution Steps

The isotope ${ }^{13} \mathrm{C}$ is a carbon atom with a mass number of 13. This means it has a total of 13 protons and neutrons combined. Since carbon has an atomic number of 6, it has 6 protons.

To find the number of neutrons in ${ }^{13} \mathrm{C}$, we subtract the number of protons from the mass number:

\[ \text{Number of neutrons} = \text{Mass number} - \text{Number of protons} = 13 - 6 = 7 \]

The problem states that there are \(2.22 \times 10^{24}\) electrons in the given amount of ${ }^{13} \mathrm{C}$. Since each carbon atom is neutral, the number of electrons equals the number of protons, which is 6 per atom.

To find the number of carbon atoms, we divide the total number of electrons by the number of electrons per atom:

\[ \text{Number of atoms} = \frac{2.22 \times 10^{24} \text{ electrons}}{6 \text{ electrons/atom}} = 3.70 \times 10^{23} \text{ atoms} \]

Now, we multiply the number of atoms by the number of neutrons per atom to find the total number of neutrons:

\[ \text{Total neutrons} = 3.70 \times 10^{23} \text{ atoms} \times 7 \text{ neutrons/atom} = 2.59 \times 10^{24} \text{ neutrons} \]

Final Answer