How many electrons can occupy the shell having [tex]$n=2$[/tex]?
A. 18
B. 8
C. 2
D. 6
E. 32
Answer (2)
Determine possible values for the azimuthal quantum number l when n = 2 : l = 0 , 1 .
Find possible values for the magnetic quantum number m l for each l : if l = 0 , m l = 0 ; if l = 1 , m l = − 1 , 0 , 1 .
Each combination of n , l , m l can hold 2 electrons due to the spin quantum number m s .
Calculate the total number of electrons: 2 ( l = 0 ) + 6 ( l = 1 ) = 8 .
Explanation
Problem Analysis We are asked to find the number of electrons that can occupy the shell with principal quantum number n = 2 . To solve this, we need to consider the quantum numbers that define the state of an electron in an atom.
Possible values of l For a given principal quantum number n , the azimuthal quantum number l can take values from 0 to n − 1 . In this case, n = 2 , so l can be 0 or 1.
Possible values of ml For each value of l , the magnetic quantum number m l can take values from − l to + l .
If l = 0 , then m l = 0 .
If l = 1 , then m l can be -1, 0, or 1.
Possible values of ms For each combination of n , l , and m l , there are two possible values for the spin quantum number m s : +1/2 and -1/2. This means that each unique set of n , l , and m l can hold two electrons.
Total number of electrons Now, let's count the total number of electrons:
For l = 0 and m l = 0 , we have 2 possible electrons (due to m s ). For l = 1 , we have m l = − 1 , 0 , 1 , which gives us 3 orbitals. Each orbital can hold 2 electrons, so we have 3 × 2 = 6 electrons.
Adding these up, we have 2 + 6 = 8 electrons.
Final Answer Therefore, the shell with n = 2 can hold a maximum of 8 electrons.
Examples
Understanding electron configurations is crucial in chemistry for predicting how atoms will interact to form chemical bonds. For example, knowing that the second electron shell (n=2) can hold 8 electrons helps explain why elements like oxygen (with 6 valence electrons) readily form bonds to achieve a stable octet configuration, as seen in water ( H 2 O ) or carbon dioxide ( C O 2 ). This principle extends to understanding the properties of semiconductors and the behavior of materials in electronic devices.
The shell with principal quantum number n = 2 can hold a maximum of 8 electrons. This is calculated by considering the available subshells and orbitals. Therefore, the correct answer is B. 8.
;
