Question

How much time would it take to distribute one Avogadro number of wheat grains, if ${10^{10}}$ grains are distributed each second ?

Answer 1

Hint: The value for Avogadro’s number is 6.022 $ \times {10^{23}}$. Thus, by simple division, one can find the value in seconds. Further, the value can be converted into minutes, hours, days, months and years etc by following the various time conversions.

Complete step by step answer:
For this, we should know what is the value of Avogadro’s number. After knowing the value, we just have to follow some simple steps.
We have studied that Avogadro’s number has value 6.022 $ \times {10^{23}}$.
Thus, the question means we have 6.022 $ \times {10^{23}}$ wheat grains which are to be distributed.
The next thing given in the question is that each second ${10^{10}}$ grains are distributed.
So, if we divide Avogadro's number by ${10^{10}}$; we will get our answer in seconds.
So, Number of seconds required = $\dfrac{{6.022 \times {{10}^{23}}}}{{{{10}^{10}}}}$
Number of seconds required = 6.022$ \times {10^{13}}$ seconds
This is the value in seconds which is very large. We can convert it into minutes, hours and then years by following time conversions.

We know that 1 hour has 3600 seconds.
So, number of hours required = $\dfrac{{6.022 \times {{10}^{13}}}}{{3600}}$
So, number of hours required = 1.672$ \times {10^{10}}$ hours

Further, we can convert into years as -
So, number of years required = $\dfrac{{1.672 \times {{10}^{10}}}}{{365 \times 24}}$
Number of years required = 1.9099$ \times {10^6}$ years

Thus, we require 1.9099$ \times {10^6}$ years to distribute the Avogadro’s number of grains even if we distribute ${10^{10}}$ grains each second. This is much larger than the value of Avogadro’s number.

Note: It must be noted that 1 year has 365 days and each day has 24 hours. Thus, by multiplying 365 with 24, we get the value for the total number of hours in a year.
Further, it should also be taken care of when any value in power is in the denominator and if we take it on a numerator the sign of power changes.