Question

What is the number of neutrons in a drop of water ( $ 20 $ drops= $ 1 $ ml) at $ {4^0} $ C?
A. $ 6.023\, \times {10^{22}} $
B. $ 1.338\, \times {10^{22}} $
C. $ 6.023\, \times {10^{20}} $
D. $ 7.338 \times {10^{22}} $

Answer 1

Hint :Neutrons are subatomic particles that make up one of the atomic nuclei's main constituents. They're usually represented by the letters n or no. There is no net electric charge associated with neutrons. They do, however, have a mass that is significantly larger than that of a proton.

Complete Step By Step Answer:
It is given in the question that $ 20 $ drops= $ 1 $ ml, therefore
 $ 1 $ drop of water= $ 1/20 $ mL
Density of water at $ 4 $ degree celsius= $ 1 $ g/mL
So mass of $ 1 $ drop of water=$density \times volume$= $ (1 \times 1/20) = 0.05 $ gm
Now we can calculate mass of one mole of water= $ 18 $ gm
 $ 1 $ mole of water contains = $ 6.23 \times {10^{23}} $ molecules of water(Avagadros number)
Now we can look into, $ 1 $ drop of water contains =(mass of $ 1 $ drop / $ 18 $ )moles
= $ (1/20 \times 1/18) = 0.00277\,moles $
So number of molecules in $ 1 $ drop of water = $ 0.00277 \times 6.23 \times {10^{23}} $
$=17.3 \times {10^{20\,}}molecules\,of\,{H_2}O $
$ 1 $ molecule of $ {H_2}O $ contains= $ 8\,neutrons $ (from oxygen only)
So the number of neutrons in $ 1 $ drop of water= $ 8 \times (17.3 \times {10^{20}}) = 1.38 \times {10^{22}} $ neutrons.
So we found that the correct option for the question is Option B- $ 1.338\, \times {10^{22}} $ neutrons.

Additional Information:
The positively charged protons repel each other, while the neutrons keep the nucleus together. The atomic number is the number of protons, and the atomic mass is the number of protons plus neutrons. Since hydrogen has only one proton and no neutrons, its atomic mass is 1. The difference between the atomic mass number (M) and the atomic number (N) equals the number of neutrons (Z).

Note :
The number of electrons of all non-charged atoms is equal to the number of protons. So it is said to subtract the number of protons from the mass number to get the number of neutrons.