Question

The diagram of a cubic crystal whose molecular mass = M, edge length = a, density = ρ,  is given below. N is the Avogadro number.

1. From the above given details nd the mass of this cube and also the mass of N particles?

2. By equating these two equations, try to nd out a suitable equation for the density of this cube.

Answer 1

1. Mass of cube = volume × density = a³ρ ……………. (1)

Mass of N particles = N × Mass of one particle

= N × \(\frac{M}{N_A}\) (M = Gram Atomic Mass) …………. (2)

2. The equations (1) & (2) represent the mass of the cube.

i.e., a³ρ = N × \(\frac{M}{N_A}\)

∴ ρ = \(\frac{N\times M}{a^3\times N_A}\)