Question

trudy writes an expression to calculate the mass defect of a carbon-14 nucleus using the symbols in the table.

quantity	symbol
mass of proton	$m_{\text{p}}$
mass of neutron	$m_{\text{n}}$
mass of electron	$m_{\text{e}}$

which expression should trudy write?

• $(6m_{\text{p}} + 8m_{\text{n}}) - m_{\text{c-14}}$
• $(8m_{\text{p}} + 6m_{\text{n}}) - m_{\text{c-14}}$
• $m_{\text{p}} + m_{\text{n}} - m_{\text{c-14}}$
• $6m_{\text{p}} + 8m_{\text{e}} - m_{\text{c-14}}$

Explanation:

Step1: Recall mass defect formula

Mass defect is the difference between the sum of the masses of protons and neutrons in the nucleus and the actual mass of the nucleus. For carbon - 14, the atomic number (number of protons) is 6, and the mass number is 14. So the number of neutrons is \(14 - 6=8\).

Step2: Calculate sum of proton and neutron masses

The mass of one proton is \(m_p\), so the mass of 6 protons is \(6m_p\). The mass of one neutron is \(m_n\), so the mass of 8 neutrons is \(8m_n\). The sum of the masses of protons and neutrons is \(6m_p + 8m_n\).

Step3: Find mass defect expression

The mass defect is the sum of the masses of protons and neutrons minus the mass of the carbon - 14 nucleus (\(m_{C - 14}\)). So the expression for mass defect is \((6m_p+8m_n)-m_{C - 14}\).

Answer:

\((6m_p + 8m_n)-m_{C - 14}\) (corresponding to the first option)