Question

The size of the nucleus is of the order of (A) \(10^{-10} \mathrm{~m}\) (B) \(10^{-14} \mathrm{~m}\) (C) \(10^{-19} \mathrm{~m}\) (D) \(10^{-3} \mathrm{~m}\)

Short answer

The size of the nucleus is of the order of (B) \(10^{-14} m\). This is because the nucleus is much smaller than the overall size of an atom but larger than a single proton or neutron. The other options represent sizes of an entire atom, a single proton or neutron, or an irrelevant large size, respectively.

Step-by-step solution

Understand how to measure atomic size

The nucleus's size is generally expressed in terms of an atomic radius, typically given in units of meters.

Recall from Atomic Physics

It is known from atomic physics that the atomic radii vary in the picometer (one trillionth of a meter, \(10^{-12} m\)) range. However, the nucleus, which is located at the center of the atom, is much smaller than the overall size of an atom, but larger than a single proton or neutron.

Use the order of magnitude approach

The order of magnitude is an approximation technique that provides a broad estimate of a number. Here, we don't need an exact value but the order of magnitude of the size of a nucleus.

Identify the appropriate order of magnitude

Given these facts from atomic physics, and looking at the options, it is clear that the size of a nucleus would be on the order of \(10^{-14} m\). So, the correct answer is (B) \(10^{-14} m\).

Explanation for the further options

To understand why the other options aren't correct: Option (A) \(10^{-10} m\), is close to the size of a whole atom, which is considerably larger than just the nucleus. Option (C) \(10^{-19} m\), is even smaller than a single proton or neutron, which doesn't make sense for the size of a nucleus, which contains several such particles. Lastly, option (D) \(10^{-3} m\), is equivalent to a millimeter which is too large by many orders of magnitude.

Key concepts

Atomic Physics

Atomic physics is the study of atoms as an isolated system of electrons and an atomic nucleus. It aims to understand the properties and behavior of atoms. A crucial part of atomic physics is knowing the structure and dynamics of atoms, focusing on electron arrangements and interactions with the nucleus.
Understanding these interactions helps in explaining phenomena such as energy levels, ionization, and spectra. When discussing atomic physics, it's essential to recognize the atom's components: electrons orbiting an immensely small but massive nucleus.
The nucleus contains protons and neutrons, which play a vital role in determining an atom’s identity and stability. In atomic physics, the precise understanding of the nucleus's size is fundamental, especially when calculating the atom's overall dimensions and understanding its forces.

Order of Magnitude

The concept of "order of magnitude" is a useful tool in physics for making approximate comparisons between different quantities. It refers to a class within a logarithmic scale, specifically powers of ten. This method helps in simplifying complex calculations by focusing on the scale or size, rather than precise measurements.
In dealing with very small or very large numbers, such as the size of a nucleus, determining the order of magnitude can quickly indicate how one quantity compares to another. For example:

• A measurement of 1 meter is on the order of magnitude of 10⁰.
• Similarly, a nucleus with a size on the order of magnitude of 10^-14 meters highlights its proportion compared to a whole atom of approximately 10^-10 meters.

By using orders of magnitude, physicists can quickly communicate and compare sizes in a meaningful manner without delving into detailed calculations.

Atomic Radius

The atomic radius describes the size of an atom from its nucleus to the boundary of the surrounding cloud of electrons. Typically measured in picometers (\(10^{-12} m \)), the atomic radius helps illustrate how atoms form molecules and engage in chemical reactions.
Atomic radii vary across different elements and are influenced by electron arrangements and nuclear charge. For example:

• Atoms with fewer electrons tend to have smaller radii due to lesser electron-electron repulsion.
• The nucleus's positive charge holds electrons closer, reducing the radius.

It's important to differentiate between the atomic radius and the nuclear size, as the nucleus is much smaller. Understanding these differences clarifies how atoms interact with each other and fits into larger structures.

Nucleus

The nucleus is a dense region at the center of an atom that contains protons and neutrons, collectively known as nucleons. It accounts for almost all the atom's mass, despite being remarkably small. The typical size of a nucleus is on the order of magnitude of 10^-14 meters.
Due to its compact size, the nucleus holds significant importance in atomic physics because:

• It determines the identity of the element via the number of protons (atomic number).
• It influences the overall atomic mass with its nucleons.
• Force interactions involving the nuclear strong force govern its stability.

These elements highlight the nucleus's critical role as it lies at the core of understanding not just the atom, but also how different atoms bond and interact at the microscopic level.