Question
Download Solution PDFThe ratio of the volume of an atom to the volume of the nucleus is (in terms of order of magnitude):
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
As atom is considered to be spherical, therefore formula to calculate volume of an atom is
- \(V_a=\frac{4}{3}\pi r_a^3\)
- Radius of atom is \(r_a=10^{-10}m\)
Again, nucleus is also considered as spherical in shape, so formula to calculate volume of nucleus is
- \(V_n=\frac{4}{3}\pi r_n^3\)
- Radius of nucleus is \(r_n=10^{-15}m\)
Explanation:
\(V_a=\frac{4}{3}\pi r_a^3=\frac{4}{3}\pi (10^{-10})^3\)
\(V_n=\frac{4}{3}\pi r_n^3=\frac{4}{3}\pi (10^{-15})^3\)
\(\frac{V_a}{V_n}=\frac{\frac{4}{3}\pi (10^{-10})^3}{\frac{4}{3}\pi (10^{-15})^3}\)
\(\frac{V_a}{V_n}=\frac{\frac{4}{3}\pi (10^{-30})}{\frac{4}{3}\pi (10^{-45})}\)
\(\frac{V_a}{V_n}=10^{15}\)
Hence, the correct answer is Option-3-\(10^{15}\).
Last updated on May 26, 2025
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