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

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Solution

Space occupied can be expressed in terms of volume of the proton.
Volume of the proton= $\frac{4}{3} Π (1.5 \times 10^{- 15})^{3}$
Total volume of $H -$ atom= $\frac{4}{3} Π (0.05 \times 10^{- 9})^{3}$
$∴$ Space occupied= $\frac{Volume of proton}{Total volume of atom}$
$= {(\frac{1.5 \times 10^{- 15}}{5 \times 10^{- 11}})}^{3} = (3 \times 10^{- 5})^{3}$
$= \frac{2.7 \times 10^{- 14}}{1}$ .

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

Space occupied can be expressed in terms of volume of the proton.Volume of the proton= 43Π(1.5×10−15)3Total volume of H−atom= 43Π(0.05×10−9)3∴ Space occupied= Volume of protonTotal volume of atom=(1.5×10−155×10−11)3=(3×10−5)3=2.7×10−141 .

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