How many Al atoms thick is the aluminum foil if it is 0.00157cm thick.
1 Al atom = 286pm
Convert pm to m
286pm = 2.86*10^-10m
Convert m to cm
2.86*10^-10m = 2.9*10^-8cm
Divide aluminum thickness and Al atom thickness
1.57*10^-3 / 2.9*10^-10 = 54138
So the aluminum foil is 54138 Al atoms thick?
Am I correct? If not please correct me!
Thank you very much.
1 Al atom = 286pm
Convert pm to m
286pm = 2.86*10^-10m
agreed
Convert cm to m
0.00157 cm
0.00157 cm/10^2 cm m^-1
=0.0000157 m
Divide aluminum thickness and Al atom thickness
1.57*10^-5 m / 2.9*10^-10 m = 54138 atoms
so looks OK. It is a good idea to keep units in calculations so you can make sure that the units cancel.
Well, if my calculations are correct, it seems like you've made a small mistake at the end. Instead of dividing the aluminum thickness by the Al atom thickness, you should actually be dividing the Al atom thickness by the aluminum thickness:
2.9*10^-8 cm / 1.57*10^-3 cm = approximately 1.8*10^4
Therefore, the aluminum foil is approximately 18,000 Al atoms thick.
Keep in mind, though, that this is just an estimate and it assumes that the atoms are perfectly stacked without any gaps or overlaps. In reality, it may not be exactly 18,000 atoms, but it's a good ballpark figure!
Hope that clears things up.
You are almost correct. Let's go through the calculations step-by-step to verify the answer.
Given:
Thickness of aluminum foil = 0.00157 cm
1 Al atom = 286 pm
First, we need to convert picometers (pm) to centimeters (cm).
1 pm = 1×10^-12 cm (conversion factor)
286 pm = 286×10^-12 cm = 2.86×10^-10 cm
Now, let's divide the thickness of the aluminum foil by the thickness of 1 Al atom.
0.00157 cm ÷ 2.86×10^-10 cm = 5.48×10^6
Therefore, the aluminum foil is approximately 5.48 x 10^6 Al atoms thick.
So, your answer should be 5.48 x 10^6, not 54138.
Your calculations are mostly correct, but there is a small mistake in your final answer.
Let's go through the calculations step by step:
First, you correctly converted 286 picometers (pm) to meters (m):
286 pm = 2.86 x 10^-10 m
Then, you converted meters (m) to centimeters (cm):
2.86 x 10^-10 m = 2.86 x 10^-8 cm
Next, you divided the thickness of the aluminum foil (0.00157 cm) by the thickness of one Al atom (2.86 x 10^-8 cm):
0.00157 cm ÷ 2.86 x 10^-8 cm = 54.895
Now, you made a small rounding error in your answer. Let's correct it:
The aluminum foil is approximately 54.895 Al atoms thick.
So, the correct answer is that the aluminum foil is approximately 54.895 Al atoms thick.
Well done with your calculations!