# Class 11 Physics Unit & measurment: NCERT Solutions for Question 27

This page focuses on the detailed Unit & measurment question answers for Class 11 Physics Unit & measurment, addressing the question: '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 ?'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 27

## 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 ?

Diameter of sodium atom = Size of sodium atom = 2.5 Å

Radius of sodium atom, r = 1/2 x 2.5 Å = 1.25 Å

= 1.25 × 10-10 m

Volume of sodium atom, V = 4/3 πr3

= 4/3 x 22/7 x (1.25 × 10-10) 3

According to the Avogadro hypothesis, one mole of sodium contains 6.023 × 1023 atoms and has a mass of 23 g or 23 × 10-3 kg.

∴ Mass of one atom = 23 × 10-3  / 6.023 x 10-3 kg

Density of sodium atom, p =

It is given that the density of sodium in crystalline phase is 970 kg m-3.

Hence, 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. Thus, the inter-atomic separation is very small in the crystalline phase.