Let's analyze the given isotopes of phosphorus: [tex]${}^{31}P$[/tex] and [tex]${}^{32}P$[/tex], and determine the correct comparison between them.
1. Atomic Number and Protons:
- The atomic number of phosphorus (P) is 15, which means each phosphorus atom has 15 protons, regardless of the isotope.
2. Mass Number:
- The mass number of an isotope is the sum of the number of protons and neutrons in the nucleus.
- For [tex]${}^{31}P$[/tex], the mass number is 31.
- For [tex]${}^{32}P$[/tex], the mass number is 32.
3. Number of Neutrons:
- To determine the number of neutrons in each isotope, we subtract the number of protons from the mass number.
- For [tex]${}^{31}P$[/tex]: Number of neutrons = Mass number - Number of protons = 31 - 15 = 16.
- For [tex]${}^{32}P$[/tex]: Number of neutrons = Mass number - Number of protons = 32 - 15 = 17.
Now, let's evaluate the options:
A. [tex]${}^{31}P$[/tex] has 16 protons, whereas [tex]${}^{32}P$[/tex] has 17 protons.
- This statement is incorrect because both isotopes have the same number of protons, which is 15.
B. [tex]${}^{31}P$[/tex] has 31 neutrons, whereas [tex]${}^{32}P$[/tex] has 32 neutrons.
- This statement is incorrect because [tex]${}^{31}P$[/tex] has 16 neutrons and [tex]${}^{32}P$[/tex] has 17 neutrons.
C. [tex]${}^{31}P$[/tex] has 16 neutrons, whereas [tex]${}^{32}P$[/tex] has 17 neutrons.
- This statement is correct. Based on our calculations, [tex]${}^{31}P$[/tex] has 16 neutrons and [tex]${}^{32}P$[/tex] has 17 neutrons.
D. [tex]${}^{31}P$[/tex] has 31 protons, whereas [tex]${}^{32}P$[/tex] has 32 protons.
- This statement is incorrect because both isotopes have 15 protons.
The correct answer is:
C. [tex]${}^{31}P$[/tex] has 16 neutrons, whereas [tex]${}^{32}P$[/tex] has 17 neutrons.
