How many electrons can fit in the orbital for which $n = 3$ and $l = 1$ ?

Question

An element 'M' has 25% of the electrons filled in the third shell as in the second shell. The element 'M' is :

Answer 1

To determine how many electrons can fit in an orbital with quantum numbers $ n = 3 $ and $ l = 1 $, we need to understand the quantum numbers and how they define electron configuration in an atom:

Principal Quantum Number ($ n $): Indicates the main energy level or shell. For $ n = 3 $, we are focusing on the third energy level.
Azimuthal Quantum Number ($ l $): Defines the shape of the orbital. The value $ l = 1 $ corresponds to a 'p' orbital. The values of $ l $ range from 0 to $ n-1 $. For $ n = 3 $, $ l $ can be 0, 1, or 2 (corresponding to 's', 'p', and 'd' orbitals, respectively).
Magnetic Quantum Number ($ m_l $): Ranges from $-l$ to $+l$, inclusive. It defines the orientation of the orbital in space. For $ l = 1 $, $ m_l $ can be -1, 0, or +1. This means there are three different orientations of the 'p' orbitals (commonly referred to as p_x, p_y, and p_z).
Spin Quantum Number ($ m_s $): Determines the spin of the electron. It can be either $\frac{1}{2}$ or $-\frac{1}{2}$. Each orbital can thus hold two electrons, one with each spin state.

Since we are dealing with $ l = 1 $ (a 'p' orbital), and there are three possible orientations for 'p' orbitals mentioned above (p_x, p_y, and p_z), each orbital can hold 2 electrons (one with spin up and another with spin down), totaling:

3 \times 2 = 6 electrons

Therefore, a total of 6 electrons can fit in the orbital described by $ n = 3 $ and $ l = 1 $ (i.e., the 3p subshell). This matches the given correct answer: 6.

Answer 2

To determine how many electrons can fit in an orbital with quantum numbers $ n = 3 $ and $ l = 1 $, we need to understand the quantum numbers and how they define electron configuration in an atom:

Principal Quantum Number ($ n $): Indicates the main energy level or shell. For $ n = 3 $, we are focusing on the third energy level.
Azimuthal Quantum Number ($ l $): Defines the shape of the orbital. The value $ l = 1 $ corresponds to a 'p' orbital. The values of $ l $ range from 0 to $ n-1 $. For $ n = 3 $, $ l $ can be 0, 1, or 2 (corresponding to 's', 'p', and 'd' orbitals, respectively).
Magnetic Quantum Number ($ m_l $): Ranges from $-l$ to $+l$, inclusive. It defines the orientation of the orbital in space. For $ l = 1 $, $ m_l $ can be -1, 0, or +1. This means there are three different orientations of the 'p' orbitals (commonly referred to as p_x, p_y, and p_z).
Spin Quantum Number ($ m_s $): Determines the spin of the electron. It can be either $\frac{1}{2}$ or $-\frac{1}{2}$. Each orbital can thus hold two electrons, one with each spin state.

Since we are dealing with $ l = 1 $ (a 'p' orbital), and there are three possible orientations for 'p' orbitals mentioned above (p_x, p_y, and p_z), each orbital can hold 2 electrons (one with spin up and another with spin down), totaling:

3 \times 2 = 6 electrons

Therefore, a total of 6 electrons can fit in the orbital described by $ n = 3 $ and $ l = 1 $ (i.e., the 3p subshell). This matches the given correct answer: 6.

How many electrons can fit in the orbital for which $n = 3$ and $l = 1$ ?

The Correct Option is B

Solution and Explanation

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