Problem 14 - A Complete Resource Book in Chemistry for JEE Main

Question

The first ionization potential will be maximum for (a) uranium (b) iron (c) hydrogen (d) lithium

Step-by-Step Solution

Answer

The first ionization potential is maximum for hydrogen (c).

Step 1: Understanding Ionization Potential

Ionization potential (or ionization energy) is the energy required to remove an electron from a neutral atom in its gaseous state. The ionization potential depends on the balance between nuclear charge and the electron's distance from the nucleus.

Step 2: Analyzing Each Element

We need to consider the position of each element on the periodic table. Hydrogen is a very small atom with only one electron, which is close to the nucleus. Iron and uranium are heavier elements and have more distant electrons due to their larger atomic size. Lithium has more electrons than hydrogen, but less than iron and uranium.

Step 3: Comparing Nuclear Factors

Hydrogen has the highest effective nuclear charge for its single electron, making its first ionization energy relatively high. Iron and uranium, although having high nuclear charges, have many shielding electrons, reducing their effective nuclear charge felt by the valence electron. Lithium also has a greater nuclear charge than hydrogen but due to its extra electron shell, its ionization energy is lower compared to hydrogen.

Step 4: Evaluating Ionization Energies

Hydrogen, having only one electron and a high effective nuclear charge, will have its electron tightly bound to the nucleus, leading to a high ionization energy. For iron and uranium, because of their larger number of inner electrons, the outer electrons are less tightly held. This effect is similar for lithium as well but less pronounced than in larger atoms like uranium and iron.

Step 5: Conclusion and Answer

Considering the small size, high nuclear charge relative to shielding, and lack of inner electron interference, hydrogen will exhibit the highest first ionization energy among the listed options.

Key Concepts

Periodic Table

The Periodic Table is a systematic arrangement of elements based on increasing atomic number. One can find elements placed in rows called periods and columns known as groups. The table not only shows the order of elements but also showcases their properties. Elements in the same group share similar characteristics.
As you move from left to right across a period, the effective nuclear charge generally increases without a significant change in shielding, affecting properties like ionization energy. On the other hand, moving down a group increases the atomic size due to added electron shells, even if the nuclear charge increases.

Effective Nuclear Charge

Effective nuclear charge (Z_{ ext{eff}}) is a concept that helps explain how much nuclear charge an electron feels. This charge impacts the atom's interactions with its electrons. While the actual nuclear charge is the total positive charge of the nucleus, the effective nuclear charge is the net positive charge experienced by an electron when considering shielding by other electrons.

• The formula for effective nuclear charge is: \[ Z_{ ext{eff}} = Z - S \] where Z is the atomic number, and S is the average number of shielding electrons.
• In simpler terms, more shielding means lower effective nuclear charge and vice versa.

The higher the effective nuclear charge, the more tightly an electron is bound to the nucleus, often resulting in a higher ionization energy.

Atomic Size

Atomic size, or atomic radius, is the distance from the nucleus to the boundary of the surrounding cloud of electrons. The size of an atom affects many of its properties.

• As you move across a period from left to right, atomic size decreases. This is due to increased nuclear charge attracting electrons closer to the nucleus.
• On moving down a group in the periodic table, atomic size increases because additional electron shells are added.

A larger atomic size often means that its electrons are further from the nucleus, making them easier to remove, which decreases the ionization energy.

Electron Shielding

Electron shielding refers to the blocking of nuclear charge by inner electrons. This concept explains why outer electrons in an atom feel less attraction toward the nucleus due to the presence of inner-shell electrons.

• Elements with many inner electron shells will have significant electron shielding.
• Shielding affects the effective nuclear charge felt by an outer electron.

As shielding increases, electrons are less tightly bound to the nucleus, which translates to lower ionization energies. Understanding this helps explain difference in ionization energies between elements, especially when looking at larger atoms where the outer electrons face less nuclear attraction due to many intervening electrons.