13.14 Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms:

Substance	Atomic Mass (u)	Density ( ${10}^3\mathit{K}\mathit{g}{\mathit{m}}^{-3})$
Carbon ( Diamond)	12.01	2.22
Gold	197.00	19.32
Nitrogen (liquid)	14.01	1.00
Lithium	6.94	0.53
Fluorine (liquid)	19.00	1.14

[Hint : Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use the known value of Avogadro’s number. You should, however, not take the actual numbers you obtain for various atomic sizes too literally. Because of the crudeness of the tight packing approximation, the results only indicate that atomic sizes are in the range of a few Å].

13.14 Let the atomic mass of a substance be = M and the density of the substance be = $?$

Avogadro's number, N = 6.023 $*{10}^{23}$

Volume of N number of molecules =$\frac{4}{3}?r^{3}N$ ……. (i)

Volume of one mole of a substance =$\frac{M}{?}$  …… (ii)

Equating (i) and (ii), we get

$\frac{4}{3}?r^{3}N=\frac{M}{?}$

<p><strong>13.14 </strong>Let the atomic mass of a substance be = M and the density of the substance be = <span title="Click to copy mathml"><math><mi>? </mi></math></span></p><p>Avogadro's number, N = 6.023 <span title="Click to copy mathml"><math><mo>*</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>23</mn></mrow></mrow></msup></math></span></p><p>Volume of N number of molecules =<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>4</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac><mi>? </mi><msup><mrow><mrow><mi>r</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup><mi>N</mi></math></span> ……. (i)</p><p>Volume of one mole of a substance =<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>M</mi></mrow></mrow><mrow><mrow><mi>? </mi></mrow></mrow></mfrac></math></span> &nbsp;…… (ii)</p><p>Equating (i) and (ii), we get</p><p><span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>4</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac><mi>? </mi><msup><mrow><mrow><mi>r</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup><mi>N</mi><mo>=</mo><mi></mi><mfrac><mrow><mrow><mi>M</mi></mrow></mrow><mrow><mrow><mi>? </mi></mrow></mrow></mfrac></math></span><span title="Click to copy mathml"><br></span></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1746168429phpRb9Ofd_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1746168429phpRb9Ofd.jpeg" alt="" width="389" height="374"></picture></div></div>

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