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Chapter 1: Problem 4

What is the approximate value of the Radius of a nucleus? (a) \(10^{-14} \mathrm{~m}\) (b) \(10^{-31} \mathrm{~m}\) (c) \(10^{-19} \mathrm{~m}\) (d) \(10^{-15} \mathrm{~m}\)

Short Answer

Expert verified
The appropriate value of the radius of a nucleus is approximately \(10^{-15} \mathrm{~m}\) (option d).

Step by step solution

01

Recall the size of an atom

Atoms are typically on the order of \(10^{-10}\) meters (1 Ångström) in diameter.
02

Compare the size of a nucleus to an atom

A nucleus is much smaller than an atom. It is composed of protons and neutrons and constitutes only a tiny part of the total volume of an atom, with the electrons occupying most of the atom's space.
03

Evaluate each option

(a) \(10^{-14} \mathrm{~m}\): This value is 1000 times smaller than the diameter of a typical atom, and it is within the appropriate range for the size of a nucleus. (b) \(10^{-31} \mathrm{~m}\): This value is far too small, as it is many orders of magnitude smaller than even the Planck length. (c) \(10^{-19} \mathrm{~m}\): This value is also too small, as it is smaller than the size of a proton or neutron. (d) \(10^{-15} \mathrm{~m}\): This value is of the same order of magnitude as a femtometer, a unit commonly used to measure nuclear dimensions. Therefore, it is reasonable to consider this value.
04

Select the correct option

The appropriate value of the radius of a nucleus is approximately \(10^{-15} \mathrm{~m}\), which corresponds to the given option (d).

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