1. A nanoparticle assembler is constructed out of 500 million atoms and is able to place 2 million atoms per second.
a. How long does it take for the assembler to reproduce itself?
b. How many assemblers exist after one hour?
c. How many assemblers exist after 3 hours?
d. With the number of assemblers available after 3
hours, how long will it take them to build a device
containing 1020 atoms?
Assembler is made up of 500 million atoms.In 1 second 2 millions atoms are placed.So for 500 millions atoms to be placed ,we need (500/2 )seconds.=250 seconds.
B)1 hour has 60×60 seconds=3600 seconds.
So in 250 seconds we have 1 assembler,this means we have (1/250) Assemblers in 1 second.Therfore in 3600 seconds we will have 3600/250 =14.4 Assemblers.
C)After 3 hours we will have 3×14.4 =43.2 Assemblers.
D)2 millions atoms can be placed by 1 assembler in 1 second.So by 3 assemblers 6 million atoms can be placed in 1 second.This means that 1 atom would require 1/(6million) seconds.Therefore 1020 atoms would need
(1020)/6000000 seconds.=1.7× 10^(-4)= 170 microseconds.
Hope this helps
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