Atom Volume Calc: Find the Volume of a Lead Atom

[Kpgabriel]

Homework Statement

Lead has a mass of 11.35 g per cubic centimeter of volume, and the mass of one of its atoms is 3.439×10-25 kg. If the atoms are spherical and tightly packed, what is the volume of an individual atom? ( m3)

Homework Equations

conversions

The Attempt at a Solution

For this problem I converted the 11.35 g/cm ^3 into 11350 g/m^3 and then converted the atom from 3.439*10^-25 kg into 3.439*10^-22 g. Then I divided it by the 11350 to get m^3 and the result was 3.03*10^-26 but it appears to be wrong.

 

[Bystander]

spherical and tightly packed,

 

[PeroK]

Homework Statement

Lead has a mass of 11.35 g per cubic centimeter of volume, and the mass of one of its atoms is 3.439×10-25 kg. If the atoms are spherical and tightly packed, what is the volume of an individual atom? ( m3)

Homework Equations

conversions

The Attempt at a Solution

For this problem I converted the 11.35 g/cm ^3 into 11350 g/m^3 and then converted the atom from 3.439*10^-25 kg into 3.439*10^-22 g. Then I divided it by the 11350 to get m^3 and the result was 3.03*10^-26 but it appears to be wrong.

How many $cm$ are there in a $m$?

 

[Kpgabriel]

How many $cm$ are there is a $m$?

100 so it would be cubed to get m^3 and it would be 3.03*10^-29 which is the right answer

 

[Mathijsgri]

If 11,35 grams fit into 1 cm³ then 3.439×10-22 g will fitt into
3.439×10-22g/ 11.35= 3.03 cm³

 

[Mathijsgri]

If 11,35 grams fit into 1 cm³ then 3.439×10-22 g will fitt into
3.439×10-22g/ 11.35= 3.03 cm³

* 3.03*10-23 cm³

 

[Kpgabriel]

* 3.03*10-23 cm³

But you're looking for m^3

 

[Mathijsgri]

But you're looking for m^3

1m³= 1.000.000cm³
? = 3.03*10 - 23cm³

 

[PeroK]

But you're looking for m^3

Are you helping him now?

 

[Mathijsgri]

'crosswise multiplication table' i don't know if it is an english term, i translated it literally from dutch.

 

[Kpgabriel]

1m³= 1.000.000cm³
? = 3.03*10 - 23cm³

Right. so it would be 11.35 g/cm^3 * 1000000cm^3/1 m^3 to give 11350000 g/m^3 which you divide into 3.439*10^-22 g

 

[Kpgabriel]

'crosswise multiplication table' i don't know if it is an english term, i translated it literally from dutch.

I just call it a conversion

 

[Mathijsgri]

Right. so it would be 11.35 g/cm^3 * 1000000cm^3/1 m^3 to give 11350000 g/m^3 which you divide into 3.439*10^-22 g

keep in mind that 1 cm³ is not equalle to 1.000.000 m³

 

[PeroK]

keep in mind that 1 cm³ is not equalle to 1.000.000 m³

I don't think you're helping here. The OP has got the correct answer. Leaving aside the question of the basic volume of a sphere as opposed to the volume it occupies in a 3D array.

 

[PeroK]

100 so it would be cubed to get m^3 and it would be 3.03*10^-29 which is the right answer

I assume that's the answer on your answer sheet?

 

[Mathijsgri]

you are right i made a typo in my calculator, sorry for that.

 

[Kpgabriel]

I assume that's the answer on your answer sheet?

Yes it was a test question I got wrong so I was trying to find the correct method to the answer