Question

The metallic radius of a potassium atom is 231 pm. What is the volume of a potassium atom in cubic meters?

Answer 1

The volume of a potassium atom is approximately 7.11 x 10^-29 cubic meters.

Step-by-step explanation:

To find the volume of a potassium atom, we need to first calculate the radius of the atom. Given that the metallic radius of a potassium atom is 231 pm, we can convert this into meters by dividing by a factor of 10^12. So, the radius of the atom is 231 x 10^-12 meters.

Next, we can use the formula for the volume of a sphere to find the volume of the atom. The formula is V = (4/3)πr^3, where V is the volume and r is the radius. Substituting in the values, we get V = (4/3)π(231 x 10^-12)^3.

Finally, we can calculate the volume by performing the calculations. The volume of the potassium atom is approximately 7.11 x 10^-29 cubic meters.

Answer 2

1 pm = 10∧-10 cm
Therefore, 230 pm is equivalent to 2.3 ×10∧-8 cm.
Atom is in the shape of a sphere,
The volume of a sphere is given by 4/3πr³
Thus, volume of the atom = 4/3π( 2.3 ×10∧-8)³
= 4/3 (3.142 ×12.167×10∧-24
= 5.096 ×10∧-23 cm³
but 1m³= 1000000cm³
Therefore, the volume of the atom = 5.096 ×10∧-29 m³