Question

Suppose your hair grows at the rate of 1/26 inches per day. Find the rate at which it rows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 nm, you answer suggests how rapidly layers of atoms are assembled in this protein synthesis. Your units should be "atomic layers/sec" Hint : Use dimensional analysis

Answer 1

Answer:

11.306 nm/s

or

113.06 atomic layers/sec

Explanation:

Hello!

First we need to know how much an inch equals in nanometers and a day in seconds:

Since 1inch = 2.54cm and 1cm=10^7nm

     1 inch = 2.54 * 10^7 nm

Also 1day = 24hours = 24*60minutes = 24*60*60seconds

   1 day = 86.4 * 10^3 s

Therefore the rate at which the hair grows in nanometers per seconds is:

    1/26 in/day = (1/26) * (2.54*10^7)/(86.4*10^3) = 11.306 nm/s

 

Now, if 1 atomic layer = 0.1 nm this means that 1 nm = 10 atomic layers.

Therefore:

The rate in atomic layers is

11.306 nm/s = 11.306 (10 atomic layers)/s = 113.06 atomic layers/sec