Question

If you had a balance that could determine the mass of a proton, how many electrons would need to weigh on the same balance to measure the same mass as a single proton?

Answer 1

Hint: For both measurements common among the proton and electron. Both have mass so start calculating by taking the mass of one electron it means that, $9.109 \times {10^{ - 31}}kg$ mass of an electron makes one electron. Now calculate for one kilogram then calculate for mass of a proton. This question plot is such to test your knowledge that you well know about the masses for each particle.

Complete step-by-step answer:
Before going to the direct answer let’s understand firstly how to attempt this question. Look here it is given us a balance, with the help of balance we weigh the compound. Most commonly we use it in our labs termed as analytical to do more precise calculation. Here on one side of the balance we put the weight which is very small and on the other side we used to put the compound pinch by pinch in an analytical bottle. A long needle is there which helps us to understand that system, it moves like an old clock needle in a to and fro motion it moves in the direction where the quantity is less.

Now according to the question,we have to balance electrons and protons. Suppose we take a proton on one side of a balance and we put in small quantities of electrons on the other side of balance, so we have to give that amount of electrons which balance the other side containing a proton atom. We know that mass of proton is given as - $mass\,of\,proton = \,1.673 \times {10^{ - 27}}kg$
And mass of electron is- $mass\,of\,an\,electron\, = \,9.109 \times {10^{ - 31}}kg$

Now we have to give information about the right amount of electrons present in one proton. Our first step is to make clear that one electron is having mass of $9.109 \times {10^{ - 31}}\,kg$ , thus we can write it as
 $9.109 \times {10^{ - 31}}\,kg\,equals\,to\,1\,electron$
Then one kilogram of mass contains this amount of electrons in it. $1\,kg = \,\dfrac{1}{{9.109 \times {{10}^{ - 31}}}}electrons$
Now as mass of a proton is $1.673 \times {10^{ - 27}}kg$ it will contains by calculation-
$1\,proton\, = \,\dfrac{1}{{9.109 \times {{10}^{ - 31}}}} \times 1.673 \times {10^{ - 27}}electrons$
$1.673 \times {10^{ - 27}}kg = \,\dfrac{1}{{9.109 \times {{10}^{ - 31}}}} \times 1.673 \times {10^{ - 27}}electrons$
$ = \,0.1836\, \times {10^4}\,electrons$
$ = 1837\,electrons$

So if we put one proton on one side of our analytical balance and on the other side of balance we put $1837\,electrons$ , the needle shows a result just in between of scale. Now the analytical balance shows that we are successful in balancing protons and electrons.


Note: Don’t get confused in the calculation it is just the same as our basic mathematical word problems. For calculating the amount of electrons in one proton you have to firstly take the mass of one electron. Analytical balance has the same working as we usually see in normal old style weighing instruments in shops but here we have to balance micro particles that are electrons and protons.