Answer
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Work Step by Step
The electron configuration of an atom represents the arrangement of electrons in its energy levels or orbitals. The number of unpaired electrons in an atom is determined by the number of electrons in partially filled orbitals. An orbital is considered partially filled if it has one or more electrons with parallel spins.
a. \( 1s^{2} 2s^{2} 2p^{4} \) has 2 unpaired electrons.
In this electron configuration, the last electron is in the 2p orbital. The 2p orbital has three orbitals, each of which can hold a maximum of two electrons. In the given configuration, two of the three orbitals are singly occupied, and the third orbital is doubly occupied. Therefore, there are two unpaired electrons.
b. \( 1s^{2} 2s^{2} 2p^{6} \) has 0 unpaired electrons.
In this electron configuration, all the orbitals up to the 2p orbital are filled with electrons, following the Aufbau principle and the Pauli exclusion principle. The 2p orbital has six electrons, with opposite spins, occupying all three orbitals. Therefore, there are no unpaired electrons.
c. \( 1s^{2} 2s^{2} 2p^{4} 3s^{1} \) has 1 unpaired electron.
In this electron configuration, the last electron is in the 3s orbital. The 3s orbital can hold a maximum of two electrons, so there is only one electron in this orbital. Since there is only one unpaired electron, the answer is 1.
d. \( [\mathrm{Ar}] 4s^{2} 3d^{5} 4p^{1} \) has 6 unpaired electrons.
The electron configuration starts with the noble gas Argon (\( [\mathrm{Ar}] \)), which has a completely filled 3p orbital. After Argon, we have 4s^2, which means there are two electrons in the 4s orbital. Next, we have 3d^5, which means there are five electrons in the 3d orbital. Finally, we have 4p^1, indicating one electron in the 4p orbital.
To determine the number of unpaired electrons, we need to consider the 3d and 4p orbitals since they are not completely filled. In this case, there are five electrons in the 3d orbital, and since the 3d orbital can hold a maximum of ten electrons, there are five unpaired electrons in the 3d orbital. Similarly, there is one unpaired electron in the 4p orbital. Therefore, the total number of unpaired electrons in species d is 5 + 1 = 6.
