Q. 274.7( 11 Votes )

# Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase: 970 kg m^{-3}. Are the two densities of the same order of magnitude? If so, why?

Answer :

Given,

Diameter of the sodium atom, (d)= 2.5 Å

∴ Radius, (r) = 1.25 Å

Density of sodium in crystalline phase, (ρ_{c})= 970 kg m^{-3}

Consider every atom of sodium to be sphere,

Volume (V) = r^{3} m^{3}

∴ V = ×3.14× (1.25×10^{-10})^{3} m^{3}

≈ 8.18×10^{-30} m^{3}

We know that,

According to Avogadro law, a mole contains 6.023×10^{23} atoms.

The molecular weight of sodium atom, (M) = 23 g = 23×10^{-3} kg

Density, (ρ) = kg/m^{3}

∴ ρ = ≈ 4.67×10^{-7} kg/m^{3}

Thus,

The density of sodium in crystalline phase (ρ_{c}) is much higher than the density of general sodium in general configuration (ρ). Because, sodium atoms in crystalline phase have very less inter-atomic separation.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSIt is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 s. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of 1 s?NEXTThe unit of length on the nuclear scale is a Fermi: 1 f = 10-15 m. nuclear sizes obey roughly the following empirical relation:r = r0 A1/3where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.

RELATED QUESTIONS :

Calculate the length of the arc of a circle of radius 31.0 cm which subtends an angle of at the centre.

Physics - ExemplarCalculate the solid angle subtended by the periphery of an area of 1cm2 at a point situated symmetrically at a distance of 5 cm from the area.

Physics - ExemplarDuring a total solar eclipse the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.

Physics - Exemplar