question 3 if the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic…

question 3 if the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic - meters. (please pay attention to the expected unit: cubic - meters) select m³ 1 pts

question 3 if the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic - meters. (please pay attention to the expected unit: cubic - meters) select m³ 1 pts

Answer

Explanation:

Step1: Convert nanometers to meters

We know that $1\ nm = 1\times10^{-9}\ m$. So, $r = 0.175\ nm=0.175\times 10^{-9}\ m$.

Step2: Assume the unit - cell is a simple - cubic unit - cell (for simplicity, and the relationship between atomic radius and unit - cell edge length $a$ in simple - cubic is $a = 2r$)

$a = 2\times0.175\times 10^{-9}\ m=0.35\times 10^{-9}\ m$.

Step3: Calculate the volume of the unit - cell

The volume of a cube (unit - cell) $V=a^{3}$. So, $V=(0.35\times 10^{-9}\ m)^{3}=0.35^{3}\times(10^{-9})^{3}\ m^{3}=4.2875\times 10^{-29}\ m^{3}$.

Answer:

$4.2875\times 10^{-29}\ m^{3}$