Problem 32 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The radius of an atomic nucleus is of the order of: (a) \(10^{-10} \mathrm{~cm}\) (b) \(10^{-13} \mathrm{~cm}\) (c) \(10^{-15} \mathrm{~cm}\) (d) \(10^{-8} \mathrm{~cm}\)

Step-by-Step Solution

Answer

(b) \(10^{-13} \mathrm{~cm}\)

Step 1: Understanding the Scale of Atomic Nucleus Size

Atomic nuclei are extremely small compared to the sizes of atoms. Atoms have a typical size on the order of angstroms, which is about \(10^{-8} \text{ cm}\). The nucleus, however, is much smaller.

Step 2: Identifying the Typical Size of a Nucleus

The size of a nucleus is commonly around femtometers (also known as fermis), which are units used when measuring nuclear scales. One fermi is equivalent to \(10^{-15} \text{ m}\), which translates to \(10^{-13} \text{ cm}\) since \(1 \text{ m} = 100 \text{ cm}\). Thus, the size of an atomic nucleus is approximately \(10^{-13} \text{ cm}\).

Step 3: Verifying the Option Against Nucleus Size

From the options given: - (a) \(10^{-10} \text{ cm}\) is too large, more akin to the size of a single atom or a few atomic radii.- (b) \(10^{-13} \text{ cm}\) is the correct scale for the radius of a nucleus.- (c) \(10^{-15} \text{ cm}\) is a typical nuclear scale in meters, but translates to \(10^{-13} \text{ cm}\) in centimeters.- (d) \(10^{-8} \text{ cm}\) is much larger, similar to atomic sizes.

Key Concepts

Femtometers

Femtometers, also known as fermis, are incredibly tiny units of measurement. Used primarily in nuclear physics to describe distances on the scale of atomic nuclei, one femtometer equals \(10^{-15}\) meters. This is because when dealing with objects as small as the nucleus of an atom, typical units like centimeters or meters are too large and impractical.

To grasp the smallness of a femtometer, consider that:

• An atomic nucleus measures approximately 1 to 10 femtometers.
• A single atom, by contrast, is measured in angstroms, which are about \(10^{-10}\) meters or 100,000 femtometers.

Thinking about such tiny distances shows just how compact these nuclear particles are. This size scale is crucial to nuclear physics, as it relates to forces and particles that operate at these microscopic levels.

Atomic Structure

Atomic structure refers to the way in which subatomic particles are arranged within an atom. An atom consists of a small, dense nucleus surrounded by a cloud of electrons. The nucleus is composed of protons and neutrons, collectively known as nucleons.

Here are some key points about atomic structure:

• The nucleus contains almost all the atom's mass, even though it takes up only a tiny fraction of the atom's volume.
• Protons in the nucleus carry a positive charge, while neutrons are neutral. This positive charge attracts the negatively charged electrons, which orbit the nucleus.
• Electrons are found in regions called electron shells or energy levels, and they define the size of the atom.

Understanding atomic structure is fundamental to grasping how atoms interact in chemical reactions and how they form molecules.

Nuclear Physics

Nuclear physics is the branch of science that explores the components and behavior of atomic nuclei. It focuses on understanding the forces that hold the nucleus together despite the repulsion between the positively charged protons.

Key areas of study in nuclear physics include:

• Nuclear forces: These are the interactions that bind protons and neutrons in the nucleus.
• Radioactivity: Some nuclei are unstable and release particles or electromagnetic radiation to reach a more stable state.
• Nuclear reactions: Processes such as fission (splitting of a nucleus) and fusion (combining nuclei) are key in both energy generation and nuclear weapons.

Nuclear physics not only reveals the nature of the smallest particles in the universe but also has practical applications, such as in medical imaging and treatment, power generation, and understanding stellar processes.