"Estimate the average mass density of asodium atom assuming its size to be about 2.5.(Use the known values of Avogadro's number and sodium's atomic mass.). Compare it with the density of sodium in its crystallinephase: 970 kg m − 3 . Are the two densities of the sameorder of magnitude? If so, why?"

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&quot;Estimate the average mass density of asodium atom assuming its size to be about 2.5.(Use the known values of Avogadro&#039;s number and sodium&#039;s atomic mass.). Compare it with the density of sodium in its crystallinephase: 970 kg       m          −      3      . Are the two densities of the sameorder of magnitude? If so, why?&quot;

Allen Ochoa · Accepted Answer

Step 1Diameter of sodium atom = Size of sodium atom =2.5. Radius of sodium atom, r=1/2 times 2.5 A=1.25 A=1.25 times 10^{-10}mVolume of sodium atom, V=      4    3   pi r^3  =      4    3    ×  3.14  ×  (  1.25  ×      10          −      10            )    3  Step 2According to the Avogadro hypothesis, one mole of sodium contains 6.023 × 1023 atoms and has a mass of 23g or 23 × 10^{-3} kg.Mass of one atom   =            23      ×              10                  −          3                            6.023      ×              10                  23                      k  gDensity of sodium atom,   ρ  =                    23        ×                  10                      −            3                                      6.023        ×                  10                      23                                              4        3            ×      3.14      ×      (      1.25      ×              10                  −          10                    )        =  4.67  ×      10          −      3        k  g      m          −      3      It is given that the density of sodium in crystalline phase is 970 kg       m          −      3      .Thus, the density of sodium atom and the density of sodium in its crystalline phase are not in the same order. This is because in solid phase, atoms are closely packed. Therefore, the inter-atomic separation is very small in the crystalline phase.

Estimate the average mass density of a sodium atom assuming its size to be about 2.5. (Use the known values of Avogadro's number and sodium's atomic mass.). Compare it with the density of sodium in its crystalline

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