The ratio of the volume of an atom to the volume of the nucleus is (in terms of order of magnitude):

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AAI ATC Junior Executive 21 Feb 2023 Shift 2 Official Paper
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  1. 1010 
  2. 1025 
  3. 1015 
  4. 10

Answer (Detailed Solution Below)

Option 3 : 1015 
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Detailed Solution

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Concept:

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-\(10^{15}\).

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