Atoms And Nuclei Question 329

Question: The nuclear radius of $ _{8}O^{16} $ is $ 3\times {{10}^{-15}} $ . If an atomic mass unit is $ 1.67\times {{10}^{-27}}kg $ , then the nuclear density is approximately

Options:

A) $ 2.35\times 10^{17}g/c{{m}^{-3}} $

B) $ 2.35\times 10^{17}kg/c{{m}^{-3}} $

C) $ 2.35\times 10^{17}c{{m}^{-3}} $

D) $ 2.35\times 10^{17}kgm{{m}^{-3}} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • For nucleus of $ _{8}O^{16} $ Mass $ =(16),(1.67\times {{10}^{-27}})kg $

Volume $ =\frac{4}{3}\pi R^{3} $

$ =\frac{4}{3}\pi {{(3\times {{10}^{-15}})}^{3}}m^{3}=36\pi \times {{10}^{-45}}m^{3} $

Density $ =\frac{mass}{volume}=\frac{16\times 1.67\times {{10}^{-27}}kg}{36\pi \times {{10}^{-45}}m^{3}} $ $ =2.35\times 10^{17}kg{{m}^{-3}} $



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