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To determine the first quantum number (often referred to as the principal quantum number, [tex]\( n \)[/tex]) of the [tex]\( 2s^2 \)[/tex] electrons in the electron configuration of phosphorus ([tex]\( \mathrm{P} \)[/tex]), let's carefully examine the given electron configuration.
The electron configuration for phosphorus ([tex]\( \mathrm{P} \)[/tex]) is:
[tex]\[ 1s^2 2s^2 2p^6 3s^2 3p^3 \][/tex]
In this electron configuration:
- The term [tex]\( 1s^2 \)[/tex] tells us there are 2 electrons in the first energy level (principal quantum number [tex]\( n = 1 \)[/tex]) in an [tex]\( s \)[/tex] orbital.
- The term [tex]\( 2s^2 \)[/tex] tells us there are 2 electrons in the second energy level (principal quantum number [tex]\( n = 2 \)[/tex]) in an [tex]\( s \)[/tex] orbital.
- The term [tex]\( 2p^6 \)[/tex] tells us there are 6 electrons in the second energy level (principal quantum number [tex]\( n = 2 \)[/tex]) in a [tex]\( p \)[/tex] orbital.
- The term [tex]\( 3s^2 \)[/tex] tells us there are 2 electrons in the third energy level (principal quantum number [tex]\( n = 3 \)[/tex]) in an [tex]\( s \)[/tex] orbital.
- The term [tex]\( 3p^3 \)[/tex] tells us there are 3 electrons in the third energy level (principal quantum number [tex]\( n = 3 \)[/tex]) in a [tex]\( p \)[/tex] orbital.
The question specifically asks for the first quantum number of the [tex]\( 2s^2 \)[/tex] electrons. Here, the [tex]\( 2s^2 \)[/tex] notation indicates that these electrons reside in the second energy level, which corresponds to the principal quantum number [tex]\( n = 2 \)[/tex].
Hence, the correct answer is:
C. [tex]\( n = 2 \)[/tex]
The electron configuration for phosphorus ([tex]\( \mathrm{P} \)[/tex]) is:
[tex]\[ 1s^2 2s^2 2p^6 3s^2 3p^3 \][/tex]
In this electron configuration:
- The term [tex]\( 1s^2 \)[/tex] tells us there are 2 electrons in the first energy level (principal quantum number [tex]\( n = 1 \)[/tex]) in an [tex]\( s \)[/tex] orbital.
- The term [tex]\( 2s^2 \)[/tex] tells us there are 2 electrons in the second energy level (principal quantum number [tex]\( n = 2 \)[/tex]) in an [tex]\( s \)[/tex] orbital.
- The term [tex]\( 2p^6 \)[/tex] tells us there are 6 electrons in the second energy level (principal quantum number [tex]\( n = 2 \)[/tex]) in a [tex]\( p \)[/tex] orbital.
- The term [tex]\( 3s^2 \)[/tex] tells us there are 2 electrons in the third energy level (principal quantum number [tex]\( n = 3 \)[/tex]) in an [tex]\( s \)[/tex] orbital.
- The term [tex]\( 3p^3 \)[/tex] tells us there are 3 electrons in the third energy level (principal quantum number [tex]\( n = 3 \)[/tex]) in a [tex]\( p \)[/tex] orbital.
The question specifically asks for the first quantum number of the [tex]\( 2s^2 \)[/tex] electrons. Here, the [tex]\( 2s^2 \)[/tex] notation indicates that these electrons reside in the second energy level, which corresponds to the principal quantum number [tex]\( n = 2 \)[/tex].
Hence, the correct answer is:
C. [tex]\( n = 2 \)[/tex]
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