Problem 74 - Master Resource Book in JEE Main Physics

Question

Assertion All nuclei are not of same size. Reason Size depends on atomic mass.

Step-by-Step Solution

Answer

The assertion is true, and it is correctly explained by the reason given.

Step 1: Understand the Assertion

The assertion states "All nuclei are not of same size," which implies that the nuclei of different atoms vary in size. This is generally true because atomic nuclei consist of protons and neutrons, and different elements have different numbers of these particles. Thus, the sizes of their nuclei differ.

Step 2: Analyze the Reason

The reason given is "Size depends on atomic mass." Atomic mass is essentially the total number of protons and neutrons in an atom, which means that larger atomic masses typically correspond to larger nuclei. This is because as you increase the number of protons and neutrons, the nucleus becomes larger.

Step 3: Determine the Relationship

To confirm if the reason supports the assertion, we check if the assertion logically follows from the reason. Since atomic mass indeed affects the number of particles in the nucleus, and more particles typically mean a larger nucleus, the reason effectively supports the assertion.

Step 4: Conclusion

The assertion is true and is supported by the reason. The statement that all nuclei are not of the same size is true, and the difference in size primarily depends on the atomic mass, which varies from element to element.

Key Concepts

Atomic Mass

Atomic mass is the measure of the total mass of an atom, which comes from its protons and neutrons. These subatomic particles have nearly equivalent mass, while electrons contribute very little due to their smaller size.
In simple terms, it is the combined average mass of an atom's protons and neutrons.

• Protons and neutrons together form the atomic nucleus.
• Each proton and neutron has a mass close to 1 atomic mass unit (amu).
• Atomic mass typically increases as more protons and neutrons are added to the nucleus.

Understanding atomic mass is important because it impacts the size and stability of the atomic nucleus. A greater atomic mass usually corresponds to a larger nucleus. This is because it contains more neutrons and protons, thereby making the nuclei of different elements vary in size.

Protons and Neutrons

Protons and neutrons are the building blocks of atomic nuclei, known collectively as nucleons. Both are found densely packed at the center of an atom.

• Protons have a positive electrical charge, while neutrons have no charge.
• These particles are nearly the same size, and their masses are almost equal.
• The number of protons (also known as the atomic number) determines the element's identity on the periodic table.

Different elements have varying numbers of protons and neutrons. Therefore, the number of these nucleons determines the size and mass of the atomic nucleus. For instance, hydrogen, the lightest element, has only one proton and potentially one neutron. In contrast, uranium has 92 protons and a substantial number of neutrons, leading to a much larger nucleus.

Atomic Nuclei

The atomic nucleus is the tiny, dense center of an atom, composed of protons and neutrons. It is the core that houses most of an atom’s mass.

• The nucleus is small compared to the overall size of the atom, but it contains nearly all the atom's mass.
• It’s held together by the strong nuclear force, one of the fundamental forces in the universe.
• The composition and structure of a nucleus determine the characteristics and behavior of an element.

As you move to heavier elements in the periodic table, you add more protons and neutrons to the nucleus, often changing its size. Each nucleus is unique in size depending on its composition, which directly relates to both its atomic mass and the number of nucleons it contains. This variability in the number of nucleons is why all atomic nuclei are not the same size.