To determine the first quantum number ([tex]\( n \)[/tex]) of a [tex]\( 3p^3 \)[/tex] electron in phosphorus, [tex]\( 1s^2 2s^2 2p^6 3s^2 3p^3 \)[/tex], let's analyze the electron configuration:
1. Understand each term in the electron configuration:
- The electron configuration for phosphorus is shown as [tex]\( 1s^2 2s^2 2p^6 3s^2 3p^3 \)[/tex].
- This notation signifies that:
- [tex]\( 1s^2 \)[/tex]: 2 electrons in the 1s orbital
- [tex]\( 2s^2 \)[/tex]: 2 electrons in the 2s orbital
- [tex]\( 2p^6 \)[/tex]: 6 electrons in the 2p orbital
- [tex]\( 3s^2 \)[/tex]: 2 electrons in the 3s orbital
- [tex]\( 3p^3 \)[/tex]: 3 electrons in the 3p orbital
2. Focus on the specific term [tex]\( 3p^3 \)[/tex]:
- The notation [tex]\( 3p^3 \)[/tex] indicates the electrons are in the third shell and in the p subshell.
- Each electron occupies an orbital characterized by a set of quantum numbers.
3. Identify the first quantum number ([tex]\( n \)[/tex]):
- The first quantum number ([tex]\( n \)[/tex]) is the principal quantum number.
- [tex]\( n \)[/tex] indicates the main energy level or shell the electron occupies.
- In the context of [tex]\( 3p^3 \)[/tex], the number before the letter corresponds to the value of [tex]\( n \)[/tex].
4. Determine [tex]\( n \)[/tex] from [tex]\( 3p^3 \)[/tex]:
- For [tex]\( 3p^3 \)[/tex], the prefix '3' represents the principal quantum number [tex]\( n = 3 \)[/tex].
Hence, the first quantum number of a [tex]\( 3p^3 \)[/tex] electron in phosphorus is:
[tex]\[ \boxed{n=3} \][/tex]
The correct answer is:
D. [tex]\( n = 3 \)[/tex].
