- The atomic number \(Z=7\) in \({}_7^{14} \text{N}\) indicates that there are 7 protons.
- In a neutral atom, the number of electrons equals the number of protons, so there are 7 electrons.
- The number of neutrons is found by subtracting the atomic number from the mass number: \(14 - 7 = 7\).
- Final count: \(\boxed{7 p^{+}, 7 e^{-}, 7 n^0}\).
Explanation
- Analyzing the Isotope Notation
To determine the number of subatomic particles for the isotope \({}_7^{14} \text{N}\), we must understand the standard notation for isotopes: \({}_Z^A \text{X}\).
In this representation:
- \(\text{X}\) is the chemical symbol of the element (in this case, \(\text{N}\) stands for Nitrogen).
- \(A\) is the mass number, which represents the total number of protons and neutrons in the nucleus.
- \(Z\) is the atomic number, which represents the number of protons in the nucleus of an atom.
From the provided notation \({}_7^{14} \text{N}\), we identify the following values:
- The atomic number \(Z = 7\).
- The mass number \(A = 14\).
- Calculating Subatomic Particles
- Protons (\(p^+\)): The atomic number \(Z\) defines the number of protons. Therefore, the number of protons is \(Z = 7\).
- Electrons (\(e^-\)): For a neutral atom, the number of electrons is equal to the number of protons. Since nitrogen-14 is neutral, the number of electrons is also \(7\).
- Neutrons (\(n^0\)): The number of neutrons is the difference between the mass number \(A\) and the atomic number \(Z\). Thus, we calculate:
\[n^0 = A - Z = 14 - 7 = 7.\]
So, the atom contains 7 neutrons.
- Final Results
Based on our analysis, the nitrogen-14 isotope (\({}_7^{14} \text{N}\)) consists of:
- Protons (\(p^+\)): 7
- Electrons (\(e^-\)): 7
- Neutrons (\(n^0\)): 7
Thus, the final results are \(\boxed{7 p^{+}, 7 e^{-}, 7 n^0}\).
Examples
Understanding the composition of atoms is fundamental to chemistry and physics. For instance, in carbon dating, scientists compare the ratio of different carbon isotopes (like Carbon-12 and Carbon-14) to determine the age of archaeological artifacts. Knowing that Carbon-12 has 6 protons and 6 neutrons while Carbon-14 has 6 protons and 8 neutrons allows researchers to measure the decay rate over time, providing a reliable method for historical dating.