To calculate the mass defect of a carbon-14 nucleus, we have to correctly account for the masses of the protons and neutrons in the nucleus and then subtract the actual mass of the carbon-14 nucleus.
First, let’s break this down step-by-step:
1. Identify the composition of a carbon-14 nucleus:
- Carbon-14 has 6 protons.
- Carbon-14 has 8 neutrons (since carbon-14 means the total mass number is 14).
2. Calculate the total mass of the protons:
- The mass of one proton is [tex]\( m_p \)[/tex].
- Since there are 6 protons, the total mass of the protons is [tex]\( 6 \cdot m_p \)[/tex].
3. Calculate the total mass of the neutrons:
- The mass of one neutron is [tex]\( m_n \)[/tex].
- Since there are 8 neutrons, the total mass of the neutrons is [tex]\( 8 \cdot m_n \)[/tex].
4. Add the masses of protons and neutrons:
- The combined mass of the protons and neutrons is [tex]\( (6 \cdot m_p) + (8 \cdot m_n) \)[/tex].
5. Subtract the actual mass of the carbon-14 nucleus:
- The actual mass of the carbon-14 nucleus is [tex]\( m_{\text{C-14}} \)[/tex].
So, the expression for the mass defect [tex]\(\Delta m\)[/tex] is:
[tex]\[ \Delta m = \left(6 m_p + 8 m_n\right) - m_{\text{C-14}} \][/tex]
Comparing this with the choices given:
1. [tex]\(\left(6 m_p + 8 m_n\right) - m_{\text{C-14}}\)[/tex]
2. [tex]\(\left(8 m_p + 6 m_n\right) - m_{\text{C-14}}\)[/tex]
3. [tex]\(m_p + m_n - m_{\text{C-14}}\)[/tex]
4. [tex]\(6 m_p + 8 m_e - m_{\text{C-14}}\)[/tex]
The correct expression is:
[tex]\[ \left(6 m_p + 8 m_n\right) - m_{\text{C-14}} \][/tex]
Therefore, the answer is the first choice.
