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Chapter 2: Problem 24

If the volume of a proton is similar to the volume of an electron, how will the densities of these two particles compare to each other?

Short Answer

Expert verified
The density ratio of a proton to an electron can be determined by taking the ratio of their masses, since their volumes are assumed to be similar. The mass of a proton is about 1.0073 atomic mass units (u), and the mass of an electron is about 0.0005485799 u. Converting to kilograms and finding the ratio, the density of a proton is approximately 1836 times greater than the density of an electron.

Step by step solution

01

1. Finding the masses of proton and electron

We need to know the masses of a proton and an electron to compare their densities. From the atomic mass unit (u), we have the following values: Mass of proton = 1.0073 u Mass of electron = 0.0005485799 u
02

2. Converting the atomic mass unit (u) to kilograms

Since density is generally given in kilograms per cubic meter (kg/m鲁), we need to convert the mass of proton and electron from atomic mass units to kilograms. The conversion factor is 1 u = \(1.66054 脳 10^{-27}\) kg. Thus, the mass of a proton in kilograms is: \(1.0073 \times 1.66054 脳 10^{-27}\) kg And the mass of an electron in kilograms is: \(0.0005485799 \times 1.66054 脳 10^{-27}\) kg
03

3. Finding the density ratio

Since the volumes of the proton and electron are similar, their ratios of densities can be found by taking the ratio of their masses: Density ratio (proton/electron) = \(\frac{Mass \thinspace of \thinspace proton}{Mass \thinspace of \thinspace electron}\) Plugging in their masses in kilograms from step 2: Density ratio (proton/electron) = \(\frac{1.0073 \times 1.66054 脳 10^{-27}}{0.0005485799 \times 1.66054 脳 10^{-27}}\) Notice that the factor \(1.66054 脳 10^{-27}\) is present in both the numerator and the denominator, so we can cancel it out. Density ratio (proton/electron) = \(\frac{1.0073}{0.0005485799}\)
04

4. Calculating the density ratio

Density ratio (proton/electron) = \(1836.152\) This means that the density of a proton is approximately 1836 times greater than the density of an electron.

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