The shell having $n=3$ contains how many subshells, how many orbitals, and up to how many electrons?
A. 3; 6; 12
B. 2; 4; 8
C. 3; 12; 36
D. 3; 9; 18
E. 3; 6; 18
Answer (2)
The number of subshells equals the principal quantum number: for n = 3 , there are 3 subshells.
The number of orbitals equals n 2 : for n = 3 , there are 3 2 = 9 orbitals.
The maximum number of electrons equals 2 n 2 : for n = 3 , there are 2 × 3 2 = 18 electrons.
Therefore, the shell with n = 3 contains 3 subshells, 9 orbitals, and up to 18 electrons.
Explanation
Problem Analysis We are asked to determine the number of subshells, orbitals, and maximum number of electrons for a shell with principal quantum number n = 3 .
Number of Subshells The number of subshells in a shell with principal quantum number n is equal to n . Therefore, for n = 3 , there are 3 subshells.
Number of Orbitals The number of orbitals in a shell with principal quantum number n is equal to n 2 . For n = 3 , the number of orbitals is 3 2 = 9 .
Maximum Number of Electrons The maximum number of electrons in a shell with principal quantum number n is equal to 2 n 2 . For n = 3 , the maximum number of electrons is 2 × 3 2 = 2 × 9 = 18 .
Final Answer Therefore, the shell with n = 3 contains 3 subshells, 9 orbitals, and up to 18 electrons.
Examples
Understanding electron configurations is crucial in chemistry for predicting how elements will interact to form compounds. For instance, knowing that the third electron shell (n=3) can hold up to 18 electrons helps us understand the electronic structure of elements like Argon (Ar), which has a full third shell and is therefore very stable and unreactive. This knowledge is also essential in designing new materials with specific electronic properties, such as semiconductors used in electronic devices.
The shell with principal quantum number n = 3 contains 3 subshells, 9 orbitals, and can hold up to 18 electrons. Therefore, the correct answer is E. 3; 9; 18.
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