Question

Which of the following statement(s) are correct? (1) The electronic configuration of \(\mathrm{Cr}\) is \([\mathrm{Ar}] 3 \mathrm{~d}^{5} 4 \mathrm{~s}^{1}\) (atomic number of \(\mathrm{Cr}=24\) ) (2) The magnetic quantum number may have a negative value (3) In silver atom, 23 electrons have a spin of one type and 24 of the opposite type (atomic number of \(\mathrm{Ag}=47)\) (4) The oxidation state of nitrogen in \(\mathrm{HN}_{3}\), is \(-3\) (a) \(1,2,3\) (b) \(2,3,4\) (c) 3,4 (d) \(1,2,4\)

Short answer

The correct statements are 1, 2, 3 (option a).

Step-by-step solution

Verify the electronic configuration of \( \mathrm{Cr} \)

Chromium (\( \mathrm{Cr} \)) has an atomic number of 24. An exception to the general rule of filling electrons, chromium's electronic configuration is \([\mathrm{Ar}] 3 d^5 4 s^1\) rather than the expected \([\mathrm{Ar}] 3 d^4 4 s^2\) due to a half-filled \( d \) subshell being more stable.

Evaluate the possibility of negative values for the magnetic quantum number

The magnetic quantum number (\(m\)) can range from \(-l\) to \(+l\), where \(l\) is the azimuthal quantum number associated with each subshell (\(s, p, d, f\)). Therefore, \(m\) may indeed have negative values.

Determine the spin orientations in a silver atom

Silver (\( \mathrm{Ag} \)) has an atomic number of 47, therefore it has 47 electrons. The electron configuration of silver can be expressed as \([ \mathrm{Kr} ] 4d^{10} 5s^1\). When filled: \(10\) electrons in \( 4d\) subshell (\(5 \) pairs with opposite spins) and \(1\) in \(5s\) gives a total of \(23\) electrons with one type of spin and \(24\) with the opposite type.

Calculate the oxidation state of nitrogen in \( \mathrm{HN}_{3} \)

To calculate the oxidation state of nitrogen in \(\mathrm{HN}_{3}\), consider that hydrogen typically has a +1 oxidation state. Let the oxidation states of the three nitrogen atoms be \(x_1, x_2,\) and \(x_3\). Solving the equation, \(+1 + x_1 + x_2 + x_3 = 0\), with known typical nitrogen oxidation states shows the total for \(\mathrm{HN}_{3}\) is not -3.

Key concepts

Chromium Electron Configuration

The electronic configuration of Chromium (symbolized as Cr) is a well-known exception to the general filling pattern of electrons. Instead of following the expected pattern of

• \([ \text{Ar}] \, 3d^4 \, 4s^2\)

Chromium adopts a configuration of

• \([ \text{Ar}] \, 3d^5 \, 4s^1\)

This seemingly unusual configuration occurs because a half-filled \(d\) subshell is more stable due to electron exchange energy and symmetry considerations. Chromium gains extra stability by promoting one electron from the \(4s\) subshell to the \(3d\) subshell, which results in this half-filled \(3d\) arrangement. The stability of such configurations is a consequence of lower energy and enhanced symmetrical distribution across available orbitals.

Quantum Numbers

Quantum numbers provide a unique "address" for each electron in an atom, defining its probable location and energy. Among these, we have the magnetic quantum number

• (denoted as \(m\)), that determines the orientation of an electron within a subshell.

The magnetic quantum number is capable of adopting a range of integer values from

• \(-l\) to \(+l\)

where \(l\) is the azimuthal (or angular momentum) quantum number related to the shape of an atomic orbital. For example, in the \(p\) subshell, where \(l = 1\), the magnetic quantum number \(m\) can be -1, 0, or +1. This negative to positive range allows electrons in each subshell to have three possible orientations, enhancing the diversity of electron distributions and contributing to the atom's magnetic characteristics.

Spin Orientation

Electrons possess a property called "spin," which is a fundamental characteristic similar to charge or mass. Spin is quantized, meaning electrons can have one of two possible orientations, often described as "spin-up"

• (+\(\frac{1}{2}\))

or "spin-down"

• (-\(\frac{1}{2}\)).

In atoms, electrons pair up in orbitals with opposite spins to minimize repulsion. For example, in a silver atom with an electron configuration of

• \([\text{Kr}] \, 4d^{10} \, 5s^1\)

we have 47 electrons in total. The \(4d\) subshell can accommodate 10 electrons, which pair up to form 5 pairs with opposite spins. Additionally, the unpaired electron in \(5s\) contributes to the overall count, resulting in an almost equal split of 23 electrons with one spin orientation and 24 with the opposite spin. This arrangement influences the magnetic properties of the atom and is essential for understanding its behavior in external fields.

Oxidation States

Oxidation states represent the hypothetical charge that an atom would have if all bonds to atoms of different elements were fully ionic. To illustrate, calculating the oxidation state requires considering known states of atoms in a molecule. For example, in hydrazoic acid (\(\text{HN}_3\)),

• hydrogen typically exhibits an oxidation state of +1.

Let the oxidation states of the nitrogen atoms be \(x_1, x_2, \) and \(x_3\). We set up the equation:

• \[+1 + x_1 + x_2 + x_3 = 0\]

This equation shows the sum of oxidation states based on charge neutrality. However, the statement that the total nitrogen oxidation in \(\text{HN}_3\) is -3 is incorrect upon deeper analysis. Proper calculations reveal a more complex distribution of partial charges across the nitrogen atoms, which demonstrates the need to verify general rules against specific configurations and molecular structures.