Respuesta :
It is given that Ta has BCC crystal structure. The density is [tex]16.6 g/cm^{3}[/tex], atomic mass is 180.9 g/mol and Avogadro's number is [tex]6.023\times 10^{23}[/tex] atoms per mol.
The expression for density is as follows:
[tex]\rho =\frac{nA}{V_{c}N_{A}}[/tex]
Here, n is number of atoms per unit cell, A is atomic number, [tex]V_{c}[/tex] is volume and [tex]N_{A}[/tex] is Avogadro's number .
Expression for volume is as follows:
[tex]V_{c}=(\frac{4R}{\sqrt{3}})^{3}=\frac{64R^{3}}{3\sqrt{3}}[/tex]
For BCC, number of atoms per unit cell is 2, putting the values,
[tex]16.6 g/cm^{3} =\frac{(2 atom)(180.9 g/mol)(3\sqrt{3})}{(64) R^{3}(6.023\times 10^{23}atom /mol)}[/tex]
On rearranging,
[tex]R^{3}=\frac{4.87\times 10^{-23} g}{16.6 g/cm^{3}}=2.938\times 10^{-24}cm^{3}[/tex]
Thus,
[tex]R=\sqrt[3]{2.938\times 10^{-24}}=1.432\times 10^{-8} cm[/tex]
Since, [tex]1 cm=10^{7} nm[/tex]
Thus, [tex]1.432\times 10^{-8} cm=0.1432 nm[/tex]
Therefore, radius of tantalum atom is 0.1432 nm.
The study of chemicals is called chemistry. The elemental weight of an atom is called atomic weight.
The correct answer to the question is 0.1432.
What is density?
- The density, of a substance is its mass per unit volume.
The data is given as follows:-
- D= 16.6g
- Na= [tex]6.023*10^{23}[/tex]
The formula used to solve the question is as follows:-
[tex]V_c =[\frac{4R}{\sqrt{3} }]^3[/tex]
Placed all the value into the question and find the value of R.
[tex]R^3 =\frac{4.87*10^{-23}}{16.6} \\\\R=\sqrt[3]{2.938*10^{-24}} \\\\=1.432*10^{-8[/tex]
Thus the correct answer is 0.1432nm.
For more information about the question, refer to the link:-
https://brainly.com/question/15209553
