To identify the correct symbol for the given radioactive nuclide, we need to follow a step-by-step process. Let's examine the details provided in the question:
1. Determine the Atomic Number (Z):
- The atomic number is defined as the number of protons in the atom.
- The atom has 15 protons.
- Therefore, the atomic number (Z) is 15.
2. Determine the Mass Number (A):
- The mass number is the sum of the protons and neutrons in the atom.
- The atom has 15 protons and 17 neutrons.
- So, the mass number (A) is calculated as:
[tex]\[
A = \text{Protons} + \text{Neutrons} = 15 + 17 = 32
\][/tex]
3. Identify the Element Symbol:
- The element is determined by its atomic number. The atomic number 15 corresponds to the element Phosphorus (P) on the periodic table.
Now, we combine the atomic number (subscript), mass number (superscript), and the element symbol to write the symbol for this radionuclide.
The correct symbol is written as:
[tex]\[
{ }_{Z}^{A} \text{ElementSymbol}
\][/tex]
Substituting the values we have determined:
[tex]\[
{ }_{15}^{32} P
\][/tex]
Therefore, the correct symbol for the given radioactive nuclide is:
[tex]\[
{ }_{15}^{32} P
\][/tex]
The correct choice from the given options is:
[tex]\[
{ }_{15}^{32} P
\][/tex]
