If a gold atom has a radius of 145 pm, and you could string gold atoms like beads on a thread, how many......?

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If a gold atom has a radius of 145 pm, and you could string gold atoms like beads on a thread, how many atoms would you need to have a necklace 36 cm long?

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Answer 1

1 pm= 1.oE-10

145pm=145*10^-10

atoms reqd=36/145*10^-10=0.000000000024

Answer 2

First recognize that you need to multiply the radius by two to get the diameter of a gold atom (145x2 = 290pm).  Next comes the tough part:

One picometer is equal to 1x10^-12 meters and one meter is equal to 1x10^2 centimeters.  To find picometers per centimeter, multiply pm/m by m/cm to get pm/cm:

(1pm/1x10^-12m)x(1m/1x10^2cm) = 1x10^10pm/cm

Now we perform a series of conversions based upon the information we have:

36cm x (1x10^10pm/cm) x (1 gold atom/290pm) = 4.28x10^6 gold atoms

Hope this helps.