Manipal Medical Manipal Medical Solved Paper-2013

  • question_answer
    The density of solid argon is 1.65 g per cc at\[-233{}^\circ C\]. If the argon atom is assumed to be a sphere of radius\[1.54\times {{10}^{-8}}cm,\]the percentage of empty space in solid argon is

    A)  32%   

    B)  54%    

    C)  68%   

    D)  62%

    Correct Answer: D

    Solution :

     Volume of one atom \[=\frac{4}{3}\pi {{r}^{3}}\] \[=\frac{4}{3}\times \frac{22}{7}\times {{(1.54\times {{10}^{-8}})}^{3}}c{{m}^{3}}\] \[=1.53\times {{10}^{-23}}c{{m}^{3}}\] Volume of all atoms in 1.65 g Ar \[=\frac{165}{40}\times 6.02\times {{10}^{23}}\times 1.53\times {{10}^{-23}}c{{m}^{3}}\] \[=0.380\text{ }c{{m}^{3}}\] Volume of solid Ar containing \[1.65\text{ }g=1\text{ }c{{m}^{3}}\] Empty space\[=1-0.380=0.620\] % = 62%


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