To determine the symbol of the given radioactive nuclide, we need to follow a series of steps based on the provided information.
### Step 1: Identify the Atomic Number
- The atomic number is equal to the number of protons in the nucleus.
- From the table, we see that the number of protons is 11.
The atomic number 11 corresponds to the element Sodium (Na) on the periodic table.
### Step 2: Calculate the Mass Number
- The mass number is the sum of the number of protons and neutrons in the nucleus.
- From the table, the number of neutrons is given as 13.
Thus, the mass number [tex]\( A \)[/tex] is calculated as:
[tex]\[ A = \text{Number of Protons} + \text{Number of Neutrons} \][/tex]
[tex]\[ A = 11 + 13 \][/tex]
[tex]\[ A = 24 \][/tex]
### Step 3: Write the Isotope Notation
The isotope notation includes the element symbol (which we determined to be Na), the atomic number (11) as a subscript, and the mass number (24) as a superscript.
So, the isotope notation is:
[tex]\[ \mathbf{{}_{11}^{24} \text{Na}} \][/tex]
### Step 4: Match with the Given Choices
We now match our isotope notation with the given choices:
1. [tex]\({}_{11}^{24} \text{Na} \)[/tex]
2. [tex]\({}_{11}^{22} \text{Na} \)[/tex]
3. [tex]\({}_{11}^{13} \text{Al} \)[/tex]
4. [tex]\({}_{13}^{24} \text{Al} \)[/tex]
The correct symbol of the radioactive nuclide, based on our calculation, is:
[tex]\[ \mathbf{{}_{11}^{24} \text{Na}} \][/tex]
### Conclusion
Thus, among the given options, the correct symbol of the radioactive nuclide is:
[tex]\[ \boxed{ {}_{11}^{24} \text{Na} } \][/tex]
