Justify the claim that the number of unpaired electron is a maximum in a given energy level.
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There are two electrons maximum in an energy level; i.e., spin +1/2 and spin -1/2 in units of h/2*Pi
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To determine the justification for the claim that the number of unpaired electrons is a maximum in a given energy level, we need to understand the electronic configuration and the principles that govern electron pairing.
In an atom, electrons are distributed in different energy levels or orbitals. The electron configuration describes how these electrons are arranged in the various orbitals.
According to the Aufbau principle, electrons fill the lowest energy orbitals first before moving to higher energy levels. Each energy level can contain a specific number of electrons based on its principal quantum number (n). The maximum number of electrons that can occupy an energy level can be calculated using the formula 2n².
When filling up the orbitals in an energy level, electrons pair up with opposite spins (spin-pairing), meaning one electron spins up (↑) while the other spins down (↓). This is known as the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of quantum numbers.
Now, let's consider the claim. In a given energy level, the maximum number of electrons it can hold is determined by the principal quantum number (n), as mentioned earlier. When all the orbitals of that energy level are being filled, the electrons will pair up until each orbital has one electron with opposite spins. Therefore, the number of unpaired electrons will be equal to half of the maximum number of electrons in that energy level.
For example, in the second energy level (n=2), there are four orbitals (s, p_x, p_y, and p_z). According to the Pauli exclusion principle, each orbital can accommodate a maximum of two electrons. So the total number of electrons that can be accommodated in the second energy level is 2n² = 2(2²) = 8 electrons. However, when filling up the orbitals, the electrons will pair up in the three p orbitals, leaving two unpaired electrons in the 2p sublevel.
Therefore, in general, the claim that the number of unpaired electrons is a maximum in a given energy level is justified by the principles of electron pairing and the structure of atomic orbitals.