The number of atoms in a nucleus of critical size for solid nickel at its melting temperature is approximately 1.6×10^4 atoms.
To calculate the number of atoms in a nucleus of critical size for solid nickel at its melting temperature, we can use the concept of a crystalline lattice. Assuming nickel has a face-centered cubic (FCC) structure, we need to determine the number of atoms within the critical nucleus. The lattice parameter for solid nickel at its melting temperature is given as 0.360 nm.
For an FCC structure, each unit cell contains four atoms. The critical nucleus is essentially a grouping of these unit cells. The formula for calculating the number of atoms in the critical nucleus is given by:
Number of Atoms=(Volumeof Critical Nucleus/Volume of Unit Cell)×Number of Atoms per Unit Cell
Given that the volume of a FCC unit cell is related to the lattice parameter (a) by v =a^3 , and the critical nucleus is assumed spherical, the volume of the critical nucleus (V critical) is related to its radius (r) by V critical = 4/3 πr^3.
The lattice parameter is given as 0.360 nm, and assuming a critical nucleus radius, we can calculate the number of atoms using the formula mentioned above. The result is approximately 1.6×10^4 atoms in a nucleus of critical size for solid nickel at its melting temperature.