Concept explainers
(a)
The density of an alpha particle’s nucleus.
(a)
Answer to Problem 1PQ
The density of an alpha particle’s nucleus is 4×1017 kg/m3_.
Explanation of Solution
Given that the radius of the constituent particle of alpha particle is 1.00 fm.
Since nuclear density is uniform, the density of alpha particle’s nucleus is the same as the density of its constituent particles.
Write the expression for density.
ρ=mV (I)
Here, ρ is the density, m is the mas, and V is the volume.
Assuming the particles to be of spherical shape, their the volume is given by the expression,
V=43πr3 (II)
Here, r is the radius.
Use equation (II) in (I).
ρ=m43πr3=3m4πr3 (III)
Conclusion:
Substitute 1.67×10−27 kg for m, and 1.00 fm for r in equation (III) to find ρ.
ρ=3(1.67×10−27 kg)4π(1.00 fm)3=3(1.67×10−27 kg)4π(1.00 fm×1 m1×1015 fm)3=4×1017 kg/m3
Therefore, the density of an alpha particle’s nucleus is 4×1017 kg/m3_.
(b)
The comparison of the density of the nucleus of an alpha particle with the density of the osmium and what this comparison say about the space between nuclei in liquids and solids.
(b)
Answer to Problem 1PQ
The density of the nucleus is about 1013 times denser than the density of osmium and this says that an atom is mostly empty space. The space between the nuclei in liquids and solids are mostly empty space as well as gases.
Explanation of Solution
It is obtained that the density of alpha particle’s nucleus is 4×1017 kg/m3. The density of osmium is 2.26×104 kg/m3.
Compare the values of the densities of nucleus and osmium.
ραρOs=4×1017 kg/m32.26×104 kg/m3=1.76×1013≈1013
Conclusion:
Therefore, the density of the nucleus is about 1013 times denser than the density of osmium and this says that an atom is mostly empty space. The space between the nuclei in liquids and solids are mostly empty space as well as gases.
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Chapter 15 Solutions
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