Calculating the diameter of a polonium atom

In summary, the conversation discusses the calculation of the diameter of solid ^{209}_{84}Po, which has a simple cubic structure at room temperature and a mass density of 9.2gcm^-3. The calculated diameter is 4.16x10^-10 m or 4.16 angstroms.
  • #1
Jenkz
59
0

Homework Statement


Polonium has a simple cubic structure at room temperature. Given that the mass density of solid [tex]^{209}_{84}[/tex]Po is 9.2gcm^-3 , calculate the diameter.

The Attempt at a Solution



Volume = mass/density = 209/ 9.2 = 22.7 cm^3

1 mole = 6.02 x10^23 mol^-1

22.7 / 6.02x10^23 = 3.77 x10^-23 cm

volume = 4/3 (pi) r^3

So diameter is 4.16x10^-10 m ?

Is this correct? I have no answers to refer to. Thank you.
 
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  • #2
It looks absolutely correct to me.
Other than the third step where you (accidentally?) put "cm" instead of "cm^3"
But the answer I think is right.

Also, angstroms would be a more convenient unit, as it is 10^(-10)m.
so the answer could be:
4.16 angstroms
 
  • #3
How would you stack balls so that they fill the whole space?
 

1. How do you calculate the diameter of a polonium atom?

The diameter of a polonium atom can be calculated using the formula D = 2r, where D is the diameter and r is the radius. The radius of a polonium atom can be determined by dividing its atomic radius (157 pm) by 2, as polonium atoms are nearly spherical in shape.

2. Is the diameter of a polonium atom always the same?

No, the diameter of a polonium atom can vary slightly depending on its atomic number and its physical state (e.g. solid, liquid, gas). However, the difference in diameter is usually very small and difficult to measure.

3. How small is the diameter of a polonium atom?

The diameter of a polonium atom is incredibly small, measuring at approximately 314 picometers (pm) or 3.14 x 10^-10 meters. This is about 100,000 times smaller than the diameter of a human hair.

4. Can the diameter of a polonium atom be measured directly?

No, the diameter of a polonium atom is so small that it cannot be measured directly using traditional laboratory equipment. Instead, it is calculated using mathematical formulas and models based on experimental data.

5. How is knowing the diameter of a polonium atom useful?

Knowing the diameter of a polonium atom is useful for understanding its physical properties, such as its atomic mass and electron configuration. Additionally, this information can be used in various fields of science, such as chemistry and nuclear physics, to study the behavior and interactions of polonium atoms with other elements.

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