For a metal specimen A with grain size number of 7 how many

For a metal specimen A with grain size number of 7, how many grains do you see under an optical microscope at a magnification of 100X?. If you observe the same number of grains for another specimen B at a magnification of 200X, what is the grain size number for specimen B?

Solution

Solution:

a) We have the formula to calculate the number of grains at 100X

N = 2^n-1

N= Number of grains

n= grain size number = 7

N= 2^7-1 = 2⁶ = 64 grains

b) To find the grain size at 200X magnification we will use this formula

N_tot = (200/100)²* 64 = 256 grains

Now using

N = 2^n-1

Log(N)= (n-1) log 2

8Log(2)/log(2) = n-1

n= 9