Question

Calculate the radius of a tantalum (ta) atom, given that ta has a bcc crystal structure, a d ensity of 16.6 g/cm3, and an atomic weight of 180.9 g/mol.

Answer 1

To determine the radius of a tantalum (Ta) atom with a bcc crystal structure, we must relate the given density and molar mass with Avogadro's number and the volume of the unit cell. By applying the density formula, calculating the number of atoms per cell, and relating edge length to atomic radius, we can calculate the desired atomic radius.

Step-by-step explanation:

To calculate the radius of a tantalum (Ta) atom with a body-centered cubic (bcc) crystal structure, we must use the given density and molar mass, along with Avogadro's number and the volume formula for bcc unit cells.

Step-by-Step Calculation

Use the formula for density (d = mass/volume) to relate the atomic mass, density, and volume of the unit cell.

Calculate the number of atoms in a bcc unit cell, which is 2.

Calculate the volume of the unit cell using the formula for the volume of a cube (V = a³, where a is the edge length), and relate it to the volume occupied by one mole of atoms using Avogadro's number (6.022×10²³atoms/mol).

Express the atomic mass in terms of grams per atom (molar mass/Avogadro's number).

Combine all equations and solve for the edge length (a) of the unit cell.

Using the relationship between the body-centered cubic cell's edge length and the atomic radius (r = (sqrt(3)/4)a), solve for the radius of the tantalum atom.

By following these steps, we'll find the radius of a tantalum atom, which helps understand the microscopic properties of the material.

Answer 2

`Ta is BCC, a=(4)/(√(3)r),n=2atoms/cell\\</p><p>p=16.6gram/cm^3,A=180.9gram/mol\\</p><p>P=(A* n)/(N_(a)* v)=(180.9(gram)/(mol)* 2 (atom)/(cell))/(6.023*10^23(atom)/(mol)*((4)/(√(3)* r))^3(cm^3)/(cell))\\</p><p>=16.6(gram)/(cm^3)\\</p><p>r=((180.9*2)/(16.6*6.023*10^23*((4)/(√(3)))^3))^(1)/(3)*10^8`