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# Calculating the fraction of space in an atom.?

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The approximate radius of a H-atom is 0.05nm, and that of a proton is 1.5 x 10^-15m. Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by nucleus.

Aug 2, 2017

#1
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Hi rosala!

Calculating the fraction of space in an atom.?

The approximate radius of a H-atom is 0.05nm, and that of a proton is 1.5 x 10^-15m. Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by nucleus.

$$\frac{radius\ of\ a\ H-atom}{radius\ of\ a\ proton}=\frac{0.05nm}{1.5\times 10^{-15}m}\times\frac{10^{-9}m}{nm}=\frac{0.000\ 000\ 000\ 050}{1.5\times10^{-15}}\\ \color{blue}=\frac{1}{0.000\ 030}$$

The volumes behave like the third power of the radii.

$${\color{blue}\frac{volum\ of\ a\ H-atom}{volum\ of\ a\ proton}}=(\frac{1}{0.000\ 030})^3\\ \color{blue}=\frac{1}{0.000\ 000\ 000\ 000\ 027}=\frac{1}{2.7\times 10^{-14}}$$

!

Aug 2, 2017
#2
+11854
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Hey asinus, thats for taking out the time to answer my question...looks like you placed the two thing in the wrong way, the volume of proton was supposed to be over that of the atom, i figured it out , thank you....btw the answer is 3 x 10-5 , i dont know why you got that, you might want to check it or you may leave it as it is, your wish , and once again thanks

Aug 2, 2017
#3
+7817
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Hi rosala!
The proton is the nucleus in the hydrogen atom.
It is, of course, much smaller than the atom of which it is a component.

The hydrogen atom (r = 0.05 nm = $$5\times 10^{-11}m$$) is much larger than

the proton ($$r=1.5\times 10^{-15}m$$ )