- The isotope \({}_{28}^{59} \text{Ni}\) has an atomic number \(Z=28\) and a mass number \(A=59\).
- The number of protons is equal to the atomic number: \(p^{+} = 28\).
- In a neutral atom, the number of electrons equals the number of protons: \(e^{-} = 28\).
- The number of neutrons is the mass number minus the atomic number: \(n^{0} = 59 - 28 = 31\).
- Final count: \(\boxed{28 \, \text{p}^{+}, 28 \, \text{e}^{-}, 31 \, \text{n}^{0}}\).
Explanation
- Analysis of Isotope Notation
The isotope notation \({}_{28}^{59} \text{Ni}\) contains key information about the composition of a nickel-59 atom. The subscript \(Z\) is the atomic number, which corresponds to the number of protons in the nucleus of the atom. The superscript \(A\) represents the mass number, which is the sum of the protons and neutrons in the nucleus. For a neutral atom, the number of electrons is equal to the number of protons.
- Determining Protons and Electrons
From the notation \({}_{28}^{59} \text{Ni}\), we can identify the atomic number \(Z = 28\). By definition, the number of protons is equal to the atomic number:
\[\text{Number of protons} (p^{+}) = Z = 28\]
Since the atom is neutral, the number of electrons is equal to the number of protons:
\[\text{Number of electrons} (e^{-}) = p^{+} = 28\]
- Calculating Neutrons
The mass number \(A\) is given as 59. The number of neutrons is found by subtracting the atomic number from the mass number:
\[n^{0} = A - Z\]
\[n^{0} = 59 - 28 = 31\]
Thus, there are 31 neutrons in a nickel-59 atom.
- Final Answer
Combining these results, a nickel-59 atom consists of 28 protons, 28 electrons, and 31 neutrons.
The final counts are \(\boxed{28 \, \text{p}^{+}, 28 \, \text{e}^{-}, 31 \, \text{n}^{0}}\).
Examples
Understanding isotope composition is fundamental in fields like nuclear medicine and radiocarbon dating. For instance, in medical imaging, doctors use specific isotopes whose unique combinations of protons and neutrons result in specific radioactive decay patterns. By knowing exactly how many subatomic particles are in an isotope, scientists can predict how it will behave when used as a tracer in the body to diagnose health conditions, safely identifying targeted areas without needing invasive procedures.