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.