Converting from mass/volume to length

[dchau503]

Homework Statement

A piece of gold leaf (density 19.3 g/cm^3) weighing 1.93 mg can be beaten into a transparent film covering an area of 14.5 cm^3. what is the volume of 1.93 mg of gold? What is the thickness of the transparent film in angstroms? I only need help with the second question. The volume of 1.93 mg of gold is 10^(-4) cm^3, but I don't know how to convert to length on the second question.

Homework Equations

Angstrom=10^(-10) meters
d=mass over volume

The Attempt at a Solution

I tried to cheat by taking the third root of 14.5 cm^3 in order to get to cm:

(14.5cm^3)^(1/3)=2.44 cm

2.44 cm (10^(-2)m/1cm)(1 Angstrom/10^(-10) meters)= 2.44 x 10^8 anstroms

The answer is 690 angstroms though and i don't know how

 

[berkeman]

Homework Statement

A piece of gold leaf (density 19.3 g/cm^3) weighing 1.93 mg can be beaten into a transparent film covering an area of 14.5 cm^3. what is the volume of 1.93 mg of gold? What is the thickness of the transparent film in angstroms? I only need help with the second question. The volume of 1.93 mg of gold is 10^(-4) cm^3, but I don't know how to convert to length on the second question.

Homework Equations

Angstrom=10^(-10) meters
d=mass over volume

The Attempt at a Solution

I tried to cheat by taking the third root of 14.5 cm^3 in order to get to cm:

(14.5cm^3)^(1/3)=2.44 cm

2.44 cm (10^(-2)m/1cm)(1 Angstrom/10^(-10) meters)= 2.44 x 10^8 anstroms

The answer is 690 angstroms though and i don't know how

There is at least one typo in the problem statement. What are the units of area?

Once you fix that, the volume of the leaf is just the area multiplied by the thickness, right?

 

[Jakeus314]

Homework Statement

A piece of gold leaf (density 19.3 g/cm^3) weighing 1.93 mg can be beaten into a transparent film covering an area of 14.5 cm^3. what is the volume of 1.93 mg of gold? What is the thickness of the transparent film in angstroms? I only need help with the second question. The volume of 1.93 mg of gold is 10^(-4) cm^3, but I don't know how to convert to length on the second question.

Homework Equations

Angstrom=10^(-10) meters
d=mass over volume

The Attempt at a Solution

I tried to cheat by taking the third root of 14.5 cm^3 in order to get to cm:

(14.5cm^3)^(1/3)=2.44 cm

2.44 cm (10^(-2)m/1cm)(1 Angstrom/10^(-10) meters)= 2.44 x 10^8 anstroms

The answer is 690 angstroms though and i don't know how

One problem may be the area of 14.5... cm^3 is not area.
If I assume that to be cm^2 the problem works out fine.
I think of it as a very shallow box of gold with a volume of LxWxH where you know L and W and just need H so that the volume becomes what it's supposed to be. LxW is area, so AxH should = Volume.

Good?

 

[dchau503]

There is at least one typo in the problem statement. What are the units of area?

Once you fix that, the volume of the leaf is just the area multiplied by the thickness, right?

There's no area measurement listed in the original question. But that would make it a lot easier, if the problem did list it.

Edit: actually, the problem did say the "area of 14.5 cm^3"...but that's weird because a cubed unit signifies volume, not area.

 

[berkeman]

There's no area measurement listed in the original question. But that would make it a lot easier, if the problem did list it.

Edit: actually, the problem did say the "area of 14.5 cm^3"...but that's weird because a cubed unit signifies volume, not area.

So the units must be wrong...

 

[dchau503]

One problem may be the area of 14.5... cm^3 is not area.
If I assume that to be cm^2 the problem works out fine.
I think of it as a very shallow box of gold with a volume of LxWxH where you know L and W and just need H so that the volume becomes what it's supposed to be. LxW is area, so AxH should = Volume.

Good?

Your advice put me on the right track, but I still don't have the complete answer:

I did 14.5 cm^3 x (thickness) = 1X10^(-4) cm^3

From the equation, I solved that thickness is 6.9 x 10^(-6) cm^3. I got the right significant figures, but not the right units. How do I convert that answer into angstroms?

 

[Jakeus314]

Your advice put me on the right track, but I still don't have the complete answer:

I did 14.5 cm^3 x (thickness) = 1X10^(-4) cm^3

From the equation, I solved that thickness is 6.9 x 10^(-6) cm^3. I got the right significant figures, but not the right units. How do I convert that answer into angstroms?

14.5 cm^3 is an error on someones part.
6.9 x 10^(-6) cm^3 is not a thickness.

Solving for thickness,
14.5 cm^2 x (thickness in cm) = 1*10^(-4) cm^3
Gives a thickness in cm.
Convert that to angstroms since those are the requested units.

cm^3 / cm^2. Yields cm

 

[dchau503]

14.5 cm^3 is an error on someones part.
6.9 x 10^(-6) cm^3 is not a thickness.

Solving for thickness,
14.5 cm^2 x (thickness in cm) = 1*10^(-4) cm^3
Gives a thickness in cm.
Convert that to angstroms since those are the requested units.

cm^3 / cm^2. Yields cm

Thanks for the answer. I finally understand the problem and it's solution, even with the typo in the problem. :(

Crash-course study books frequently have mistakes in them, lol.