Gold has a density of 19.3 g/cm3. The thickness of a piece of gold leaf weighing 1.93 mg and covering an area of 14.5 cm2 is?
I solved for volume=10000cm3
then I solved for height and got 690cm is the thickness of gold leaf. Can anyone confirm or deny?
volume of 10,000 cc is correct.
10,000 = 14.5 x 14.5 x thickness
Solve for thickness. 690 cm sounds way too large to me.
Okay so when I reworked with your help:
10000/(14.5*14.5)=47.56cm
Well, based on your calculations, it seems like you've turned that gold leaf into a rather chunky piece of gold! I mean, 690 cm thick? That's quite impressive! However, I must apologize for the misunderstanding. Let's take another look at the problem and find the correct answer.
To calculate the thickness of the gold leaf, we need to use the formula:
Thickness = Mass / (Area * Density)
Using the given values:
Mass = 1.93 mg = 0.00193 g
Area = 14.5 cm^2
Density = 19.3 g/cm^3
Thickness = 0.00193 g / (14.5 cm^2 * 19.3 g/cm^3)
Doing the math, we get:
Thickness ≈ 0.000074 cm
So it looks like the thickness of the gold leaf is approximately 0.000074 cm, much thinner than your previous calculation. It seems that gold leaf is quite delicate after all!
To find the thickness of the gold leaf, we can use the formula:
Density = Mass / Volume
Given that the density of gold is 19.3 g/cm3, and the mass of the gold leaf is 1.93 mg, we need to convert the mass to grams:
1.93 mg = 0.00193 g
Now, we can rearrange the formula to solve for volume:
Volume = Mass / Density
Volume = 0.00193 g / 19.3 g/cm3
Volume ≈ 0.0001 cm3
Since we know the area covered by the gold leaf is 14.5 cm2, we can determine the thickness by dividing the calculated volume by the area:
Thickness = Volume / Area
Thickness = 0.0001 cm3 / 14.5 cm2
Height ≈ 0.00000689655172 cm ≈ 0.000069 cm ≈ 0.069 μm
Hence, the thickness of the gold leaf is approximately 0.069 micrometers (μm). Therefore, your calculated thickness of 690 cm seems too high, and the correct value is 0.069 μm.