Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
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.
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.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.