According to quantum mechanics, the maximum number of electrons in a subshell is calculated by which formula?

According to quantum mechanics, the maximum number of electrons in a subshell is calculated by which formula?

• A. 2l + 2
• B. 4l + 2
• C. 6l + 2
• D. 8l + 2

Answer: (B)

The correct answer is determined by understanding how subshells are defined in quantum mechanics and the role of quantum numbers. Each subshell is characterized by the angular momentum quantum number, \( l \). The maximum number of electrons that can occupy a given subshell is calculated using the formula \( 2l + 2 \). The reasoning behind this formula is that each subshell can accommodate multiple orbitals, with an orbital being capable of holding up to two electrons (with opposite spins). For a given subshell characterized by the value of \( l \): - The number of orbitals is determined by \( 2l + 1 \). This accounts for the different orientations of the orbitals within the subshell. - Since each orbital can hold two electrons, the total maximum capacity for electrons is then given by multiplying the number of orbitals \( (2l + 1) \) by 2, leading to the formula \( 2(2l + 1) = 2l + 2 \). This equation correctly reflects the maximum number of electrons that can occupy a subshell, based on the defined quantum numbers. Thus, the correct answer aligns with the principles of quantum mechanics regarding electron configuration in an atom.

The correct answer is determined by understanding how subshells are defined in quantum mechanics and the role of quantum numbers. Each subshell is characterized by the angular momentum quantum number, ( l ). The maximum number of electrons that can occupy a given subshell is calculated using the formula ( 2l + 2 ).

The reasoning behind this formula is that each subshell can accommodate multiple orbitals, with an orbital being capable of holding up to two electrons (with opposite spins). For a given subshell characterized by the value of ( l ):

• The number of orbitals is determined by ( 2l + 1 ). This accounts for the different orientations of the orbitals within the subshell.

• Since each orbital can hold two electrons, the total maximum capacity for electrons is then given by multiplying the number of orbitals ( (2l + 1) ) by 2, leading to the formula ( 2(2l + 1) = 2l + 2 ).

This equation correctly reflects the maximum number of electrons that can occupy a subshell, based on the defined quantum numbers. Thus, the correct answer aligns with the principles of quantum mechanics regarding electron configuration in an atom.