Let's analyze the given information to determine the correct statement about the radionuclide. Here are the details provided:
- The atom of the radionuclide contains 31 protons.
- The atom of the radionuclide contains 36 neutrons.
### Step-by-Step Solution:
1. Determine the Atomic Number:
- The atomic number of an atom is defined as the number of protons it contains.
- Given that the atom contains 31 protons, the atomic number is therefore 31.
2. Determine the Mass Number:
- The mass number of an atom is defined as the total number of protons and neutrons.
- The given atom contains 31 protons and 36 neutrons.
- Therefore, the mass number can be calculated as:
[tex]\[
\text{Mass Number} = \text{Number of Protons} + \text{Number of Neutrons}
\][/tex]
[tex]\[
\text{Mass Number} = 31 + 36 = 67
\][/tex]
3. Correct Symbol Notation:
- In the notation [tex]\(\ce{{}_Z^A \text{Element}}\)[/tex], [tex]\(Z\)[/tex] represents the atomic number, and [tex]\(A\)[/tex] represents the mass number.
- For our atom, the atomic number ([tex]\(Z\)[/tex]) is 31 and the mass number ([tex]\(A\)[/tex]) is 67.
- The chemical symbol for the element with atomic number 31 is Gallium (Ga).
- Therefore, the correct symbol notation for this radionuclide is:
[tex]\[
{}_{31}^{67} \text{Ga}
\][/tex]
4. Evaluate the Given Statements:
- Statement 1: "The atomic number is 31, the mass number is 67, and its symbol is [tex]${}_{31}^{67} Ga$[/tex]."
- This statement is correct based on our calculations.
- Statement 2: "The atomic number is 31, the mass number is 67, and its symbol is [tex]${}_{57}^{31} Ga$[/tex]."
- This statement is incorrect because the symbol notation does not match the atomic and mass numbers.
- Statement 3: "The atomic number is 67, the mass number is 31, and its symbol is [tex]${}_{31}^{67} Ga$[/tex]."
- This statement is incorrect because the atomic and mass numbers are swapped.
- Statement 4: "The atomic number is 67, the mass number is 31, and its symbol is [tex]${}_{67}^{31} Ga$[/tex]."
- This statement is incorrect because both the atomic and mass numbers are incorrect.
Based on our evaluation, the correct statement is:
"The atomic number is 31, the mass number is 67, and its symbol is ${}_{31}^{67} \text{Ga}."
