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

Oct 6, 2016

You would need 1837 electrons.

#### Explanation:

The mass of a proton is 1.673 × 10^"-27"color(white)(l) "kg".

The mass of an electron is 9.109 × 10^"-31"color(white)(l) "kg"

$\text{1 electron"/(9.109 × 10^"-31" color(red)(cancel(color(black)("kg")))) × (1.673 × 10^"-27" color(red)(cancel(color(black)("kg"))))/"1 proton" = "1837 electrons"/"1 proton}$

Thus, 1837 electrons have the same mass as 1 proton.