Question

The ratio of the radii of hydrogen atom and its nucleus is ~105 . Assuming the atom and the nucleus to be spherical, (i) what will be the ratio of their sizes? (ii) If atom is represented by planet Earth ‘Re’ = 6.4 x 106 m. Estimate the size of the nucleus.

July 11, 2024

Answer

(i) Volume of the sphere = $4\over3$ πr³

Let R be the radius of the atom and r be that of the nucleus.

⇒ R = 10⁵ r

Volume of the atom = $4\over3$ 𝜋R³ = $4\over3$ 𝜋(10⁵ r)³ (∴ R = 10⁵ r)

= $4\over3$ 𝜋r ³ × 10¹⁵

Volume of the nucleus = $4\over3$ 𝜋r ³

Ratio of the size of atom to that of nucleus = ${{4\over 3} \times 10^{15} \times \pi r^3}\over {4\over 3}\pi r^3$ = 10¹⁵

(ii) If the atom is represented by the planet Earth (Re = 6.4 x 10⁶m), then the radius of the nucleus would be

rn = $Re\over10^5$

rn = $6.4 \times 10^6m\over10^5$

= 6.4 x 10 m

= 64 m.

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