Matthew S. answered • 09/16/15
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Assuming that the number given in the subject has units of centimeters, we can go from there.
Background information that is needed to know for this question:
1 cm = 10-2 m = 108 Å (angstroms) = 104 μm
volume of a sphere is (4/3)πr3
Using dimensional analysis
2.7x10-8 cm 108 Å
---------------- x ---------- = 2.7 Å, making the radius 1.35 Å ≅ 1.4 Å
1 cm
2.7x10-8 cm 10-2 m
---------------- x ---------- = 2.7x10-10 m, or a radius of 1.4x10-10 m
1 cm
---------------- x ---------- = 2.7x10-10 m, or a radius of 1.4x10-10 m
1 cm
Assuming the third question is asking how many can be placed side by side for a distance of 2.5 μm then the diameter needs to be converted to micrometers first and that it is implied that that is the diameter per 1 atom. Using the same dimensional analysis as before, the diameter is determined to be 2.7x10-2 μm per atom. Therefore
2.5 μm / 2.7x10-2 μm = 92.59 atoms or 93 atoms (2 sig figs)
The volume of the sphere can be found using the radius we found previously in meters and the equation in the need-to-know information
(4/3)πr3 = (4/3)π(1.4x10-10 m)3 = 1.1494x10-29 m3 ≅ 1.1x10-29 m3
Matthew S.
All of those answers are in 2 sig figs. Scientific notation is the least confusing way to express correct sig figs. Take the volume, 1.1 x 10-29 m3. The "1.1" shows the number of sig figs, numbering 2, and the "x 10-29" simply represents the placeholder of the number.
1.1 x 10-29 m3 is much easier to write than 0.000000000000000000000000000011 cm3. Not to mention the order of magnitude, the "10x," is easier to keep track of.
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09/17/15
Sarah M.
09/17/15