- Identify the atomic number \(Z = 81\) from the subscript, which directly gives the number of protons.
- Recognize that in a neutral atom, the number of electrons equals the number of protons, confirming 81 electrons.
- Subtract the atomic number from the mass number \(A = 204\) to find the number of neutrons: \(204 - 81 = 123\).
- Conclude that the atom has 81 protons, 81 electrons, and 123 neutrons: \(\boxed{81 \, p^{+}, 81 \, e^{-}, 123 \, n^{0}}\).
Explanation
- Identify Protons from Atomic Number
In the chemical notation \({}_{Z}^{A}\text{X}\), \(Z\) represents the atomic number (the number of protons in the nucleus), \(A\) represents the mass number (the sum of protons and neutrons in the nucleus), and \(\text{X}\) is the chemical symbol of the element. For the isotope \({}_{81}^{204}\text{Tl}\), we identify that \(Z = 81\) and \(A = 204\). This tells us that there are 81 protons in the nucleus of this thallium atom.
- Determine Electrons in a Neutral Atom
In a neutral atom, the total electrical charge is zero, which requires the number of negatively charged electrons (\(e^{-}\)) to exactly balance the number of positively charged protons (\(p^{+}\)). Since there are 81 protons, there must also be 81 electrons to maintain electrical neutrality.
- Calculate the Number of Neutrons
The mass number \(A\) is defined as the total number of nucleons, which are the sum of protons and neutrons. We have the relationship: \(A = Z + n^{0}\), where \(n^{0}\) is the number of neutrons. Rearranging this to solve for neutrons, we get \(n^{0} = A - Z\). Substituting the given values: \(n^{0} = 204 - 81 = 123\). Therefore, the nucleus contains 123 neutrons.
- Final Answer
Based on the analysis of the isotope \({}_{81}^{204}\text{Tl}\), we have determined that it contains 81 protons, 81 electrons, and 123 neutrons. The final result is: \(\boxed{81 \, p^{+}, 81 \, e^{-}, 123 \, n^{0}}\).
Examples
Understanding isotopes is crucial in fields like medicine and archaeology. For instance, radioactive isotopes like Thallium-204 are used in industrial measurements, such as gauging the thickness of materials. By knowing the exact number of protons, electrons, and neutrons, scientists can predict how an isotope will decay and how it will interact with other matter, which is essential for safely using it in research or medical applications.