Estimate the average mass density of a sodium atom assuming its size to be about 2.5 A- (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 unit of length convenient on the nuclear scale is a fermi : 1 f = 10^(-15) m. Nuclear sizes obey roughly the following empirical relation : r = r_0A^(1/3) where r is the radius of the nucleus, A its mass number, and r_0 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.

An element with molar mass 2.7xx10^-2 kg mol^-1 forms a cubic unit cell with edge length 405pm. If its density is 2.7xx103 kg m^-3 , what is the nature of the cubic unit celL?

In a test experiment pn a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 70 m s^-1 and 63 m s^-1 respectively. What is the lift on the wing if its area is 2.5 m^2 ? Take the density of air to be 1.3 kg m^-3 .

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^-1 to 3.5 m s^-1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?

The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time f?(b) What is the kinetic energy of the air? (c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m^- 2 , v = 36 km/h and the density of air is 1.2 kg m^-3 . What is the electrical power produced?

Niobium crystallises in body-centred cubic structure. If density is 8.55 g cm^-3 , calculate atomic radius of niobium using its atomic mass 93 u.