Chapter 4, Problem 97A

Interpretation Introduction

Interpretation:

The number of times the diameter of an atom is greater than the diameter of its nucleus needs to be determined. The density of the nucleus, knowing that most of an atom’s mass is contained in the nucleus needs to be determined.

Concept introduction:

The diameter of an atom is always bigger than its nucleus, as the surrounding electrons rotates and revolves at a distance from the nucleus in different shells.

The density of an object depends on its mass.

$\mathrm{density}=\frac{mass}{volume}$

Answer to Problem 97A

The diameter of an atom is over $10,000$ times the diameter of its nucleus.

The density of an atom is all because of its nucleus, electrons contributing negligibly in it.

Explanation of Solution

A nucleus diameter is in the range of $10^{-13}-10^{-12}cm$.

The atomic diameter is about $10^{-8}cm$.

Hence, the diameter of an atom is over 10, 000 times the diameter of its nucleus.

The density of the nucleus $2.3\times 10^{17}kg/m^3$. The whole mass of an atom is known to be in the centre that is the nucleus as the mass of electron is very small in comparison to that of electron and proton, so its mass is generally taken negligible. And while calculating the mass of an atom, the masses of the proton and neutron are added. As density is directly proportional to the mass, hence they also change.

Conclusion

The diameter of an atom is over 10, 000 times the diameter of its nucleus and the density of an atom is contributed by its nucleus alone.