Problem 59 - A Complete Resource Book in Chemistry for JEE Main

Question

The total number of electrons present in all the \(\mathrm{s}\) orbitals, all the p orbitals and all the d orbitals of cesium ion are respectively (a) \(12,20,22\) (b) \(8,22,24\) (c) \(10,24,20\) (d) \(8,26,10\)

Step-by-Step Solution

Answer

Option (c): 10 (s), 24 (p), 20 (d).

Step 1: Understand the Electron Configuration of Cesium Ion

Cesium (Cs) has an atomic number of 55. It typically loses one electron to form the cation (Cs⁺), with an electronic configuration of \[\mathrm{[Xe]}\ 6s^1\rightarrow Cs^+ : [\mathrm{Xe}]\ 5s^2\ 4d^{10}\ 5p^6\].

Step 2: Count Electrons in s Orbitals

Identify the electrons in all the \(s\) orbitals. The configuration includes \( \mathrm{1s^2}, \ 2s^2, \ 3s^2, \ 4s^2, \ 5s^2 \); therefore, the total in \(s\) orbitals is \(2 + 2 + 2 + 2 + 2 = 10\).

Step 3: Count Electrons in p Orbitals

Electrons are present in \( \mathrm{2p^6}, \ 3p^6, \ 4p^6, \ 5p^6 \); thus, the total in \(p\) orbitals is \(6 + 6 + 6 + 6 = 24\).

Step 4: Count Electrons in d Orbitals

The \(d\) orbitals have electrons only in \(\mathrm{3d^{10}, \ 4d^{10}}\); therefore, the total in \(d\) orbitals is \(10 + 10 = 20\).

Step 5: Match with Provided Options

Compare the calculated electron count to each option. The total of \(s\), \(p\), and \(d\) are \(10, 24, 20\) respectively, which matches option (c).

Key Concepts

Understanding s Orbitals

In the world of atomic structure, "s orbitals" are the simplest type of atomic orbitals. They are spherical in shape and can hold up to two electrons. Every energy level in an atom has one s orbital, starting from the first energy level, denoted as 1s.

When considering electron configurations, the s orbitals play a fundamental role. They are always filled first due to their availability at the lowest energy level. As we go higher in energy levels, we move to 2s, 3s, 4s, and so on.

• A key point is that s orbitals can only hold a maximum of 2 electrons no matter the energy level.
• For example, the electron configuration of the cesium ion includes 1s², 2s², 3s², 4s², and 5s².
• Adding these, we get a total of 10 electrons in all s orbitals for a cesium ion.

The Role of p Orbitals in Electron Configuration

P orbitals have a more complex structure compared to s orbitals. They are dumbbell-shaped and each energy level from the second onwards can have a set of three p orbitals, named as px, py, and pz. Each of these can accommodate 2 electrons, allowing for a total of 6 electrons.

P orbitals come into play starting from the second energy level (2p) and continue to fill in subsequent levels like 3p, 4p, and so forth. In the electron configuration:

• P orbitals have higher energy than s orbitals within the same shell, which is why they fill after s orbitals are complete.
• For a cesium ion, the p orbitals include 2p⁶, 3p⁶, 4p⁶, and 5p⁶, with each contributing 6 electrons.
• Summing these gives us a total of 24 electrons distributed across all p orbitals.

Delving into d Orbitals

D orbitals introduce even more complexity, appearing in the third energy level but really becoming prominent from the fourth energy level onwards. Each set contains five d orbitals, each able to hold 2 electrons, so a full set can hold up to 10 electrons.

D orbitals are present in elements from the transition metal series, giving rise to their fascinating properties.

• When observing the electron configuration of a cesium ion, we see electrons in 3d¹⁰ and 4d¹⁰ orbitals.
• This results in 20 electrons housed in the d orbitals alone for cesium ion.

These electrons significantly affect the chemical properties of the ion, contributing to important characteristics like electron affinity and ionization energy.