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Chapter 38: Problem 16

Compare the radius of the proton (the \(A=1\) nucleus) with the Bohr radius of the hydrogen atom.

Short Answer

Expert verified
The Bohr radius of the hydrogen atom, which is 0.529 \(\AA\), is much larger than the radius of a proton, which is about 0.000084-0.000087 \(\AA\), after converting from femtometers to angstroms. This indicates that the hydrogen atom (according to the Bohr model) is significantly larger than a proton.

Step by step solution

01

Find the Radii in the Same Units

First, take the known radius of a proton which is 0.84-0.87 fm. This needs to be converted to angstroms for comparison. As 1 \(\AA\) is equal to 10,000 fm, we multiply the radius of the proton by this conversion factor to get the radius of the proton in angstroms.
02

Comparison of Radii

Now, compare this value with the Bohr radius of the hydrogen atom, which is 0.529 \(\AA\). The comparison will show that the Bohr radius is much larger implying that the hydrogen atom, as per the Bohr model, is much larger than the size of the proton (its nucleus).

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