Problem 47 - A Complete Resource Book in Chemistry for JEE Main

Question

Let IP stand for ionization potential. Then element for which the value of \(\mathrm{IP}_{1}, \mathrm{IP}_{2}, \mathrm{IP}_{3}, \mathrm{IP}_{4}\) are \(50,100,250\) and \(2051 \mathrm{eV}\) respectively, is (a) \(\mathrm{Al}\) (b) \(\mathrm{Na}\) (c) \(\mathrm{Mg}\) (d) \(\mathrm{Si}\)

Step-by-Step Solution

Answer

The element is Na.

Step 1: Understanding Ionization Potential

Ionization potential (IP) is the energy required to remove an electron from an isolated atom or molecule. The first ionization potential (IP1) corresponds to the removal of the first electron, the second ionization potential (IP2) corresponds to the removal of the second electron, and so on. Typically, IP values increase because the ion becomes more positively charged and electron removal becomes more difficult.

Step 2: Analyzing Ionization Potentials

The given ionization potentials are: \( \mathrm{IP_{1}} = 50 \mathrm{eV}, \mathrm{IP_{2}} = 100 \mathrm{eV}, \mathrm{IP_{3}} = 250 \mathrm{eV}, \mathrm{IP_{4}} = 2051 \mathrm{eV} \). A significant jump in ionization potential indicates removal of an electron from a stable, inner electron shell.

Step 3: Identifying the Element

Compare the provided IPs with typical behavior of known elements. For sodium (Na), the first electron removal (IP1) is from the outer shell, and the second one (IP2) involves removing from the more stable, full inner shell, resulting in a high IP. Hence, \( \mathrm{Na} \) is characterized by small \( \mathrm{IP_{1}} \), \( \mathrm{IP_{2}} \), \( \mathrm{IP_{3}} \) and a very high \( \mathrm{IP_{4}} \). This matches with our IP4 (2051 eV) value. In comparison, silicon (Si), aluminum (Al), and magnesium (Mg) would not have such a dramatic jump at \( \mathrm{IP_{4}} \). Therefore, the element is \( \mathrm{Na} \).

Key Concepts

First Ionization Energy

To truly understand ionization potential, we must first recognize what 'first ionization energy' means. This is the amount of energy needed to remove the outermost electron from a neutral atom when it is in its gaseous state.
When we talk about the 'first ionization energy' specifically, we are just looking at removing that very first electron. This process takes a specific amount of energy. This is because electrons are naturally attracted to the positive charge of the nucleus. Hence, extracting them requires adding energy to overcome this attraction.
For sodium (Na), the first ionization energy is relatively low. This is because it has only one electron in its outer shell. That electron does not hold on tightly because it's farthest from the nucleus and there are inner electrons that reduce the pull from the nucleus. But as soon as we attempt to remove additional electrons, the energy needed rises sharply because we are digging into more stable, fuller shells.

Atomic Structure

Atoms are the building blocks of matter, and their structure is fascinating! They consist of a dense nucleus filled with protons and neutrons surrounded by a cloud of electrons.
One key feature of an atom is its nucleus, which contains positively charged protons and neutral neutrons. This positively charged center attracts negatively charged electrons. These electrons orbit the nucleus in various energy levels or shells.
Each shell can hold a fixed number of electrons, and electrons will fill the lowest available energy levels before moving to higher ones. This arrangement is what gives different elements their unique properties and behavior.

• The closer an electron is to the nucleus, the more energy is needed to remove it because the attraction is stronger.
• Electrons in outer shells can be removed with less energy, which is the basis of ionization potential.

Understanding atomic structure is essential in explaining why elements like sodium have specific jumps in energy when electrons are removed.

Electron Configuration

Electron configuration describes how electrons are distributed in an atom's shells. For many students, visualizing this setup helps in comprehending why elements behave the way they do chemically.
It's a way of denoting the number of electrons in an atom, their arrangement in shells, and their subshells. Every element has a unique electron configuration that determines its chemical properties and reactions.

• Electrons fill the lowest energy levels first, in an order dictated by the Aufbau principle.
• For example, sodium, with an atomic number of 11, has an electron configuration of \( \text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^1 \).
• This means two electrons in the 1s subshell, two in the 2s, six in the 2p, and one in the 3s.

With this arrangement, it's clear why sodium's first ionization energy is relatively low. Removing the single electron in its outermost shell takes minimal energy compared to breaking a full inner shell, which would need significantly more energy.