I keep getting the wrong answer?
I know there is one similar to this on here but I keep getting the wrong answer.
The gold foil Rutherford used in his scattering experiment had a thickness of approximately 6×10^−3mm. If a single gold atom has a diameter of 2.9×10^−8 cm, how many atoms thick was Rutherford's foil?
I convert 6×10^−3mm to cm and got 6x10^-4cm
6x10^-4cm/2.9x10^-8cm= 2.0689655e-12?
is that right or did I do something wrong?
Nuts to your math.
numberatomsthick=thickness/thickone
=6E-3mm/2.9E-7mm= 6/2.9 E5 atoms.
I get 6E-3/2.9E-7 = 2E4
drBob is right, goodness, 7-3 is E4
Thank you for the help everyone!
To determine whether your calculation is correct, let's work through the problem step by step.
First, you correctly converted the thickness of the gold foil from mm to cm:
6×10^−3 mm = 6×10^−4 cm
Next, let's calculate how many gold atoms can fit in the thickness of the foil. To do this, we need to divide the thickness of the foil by the diameter of a single gold atom:
6×10^−4 cm / 2.9×10^−8 cm
When dividing two numbers in scientific notation, we subtract the exponents:
6 / 2.9 = 2.0689655
And we subtract the exponents of the powers of 10:
10^−4 / 10^−8 = 10^(−4 − (−8)) = 10^4
Putting it all together, we have:
2.0689655 × 10^4
Rounded to the appropriate number of significant figures, the answer is approximately 2.07 × 10^4.
So, based on your calculations, your answer of 2.0689655e-12 was incorrect.
To check our results, we could also use unit cancellation as a helpful tool. In this case, the centimeter (cm) units will cancel out, leaving us with the number of gold atoms.
6×10^−4 cm / 2.9×10^−8 cm = (6/2.9) × (10^−4 / 10^−8)
Simplifying the expression, we have:
2.0689655 × 10^4 atoms
Therefore, the correct answer is that Rutherford's foil was approximately 2.07 × 10^4 atoms thick.