Video Transcript
An electron has a charge of
negative 1.60 times 10 to the negative 19th coulombs and a mass of 9.11 times 10 to
the negative 31 kilograms. What is the charge-to-mass ratio of
an electron? Give your answer to three
significant figures.
This question is asking us to find
a charge-to-mass ratio, which exactly as its name suggests is an object’s charge
divided by its mass. In this case, the object we’re
interested in is an electron, and we’re given a value for its charge and also a
value for its mass. So all we need to do is plug in
negative 1.60 times 10 to the negative 19th coulombs for the charge and 9.11 times
10 to the negative 31 kilograms for the mass. To start this calculation, note
that the units will be coulombs per kilogram, which is a valid unit of
charge-to-mass ratio since it’s a unit of charge divided by a unit of mass. For the numerical part of our
answer, we plug in negative 1.60 times 10 to the negative 19th divided by 9.11 times
10 to the negative 31 into a calculator. This gives us negative 1.75631 et
cetera times 10 to the 11th with units of coulombs per kilogram.
All that’s left now is to give this
answer to three significant figures. Starting on the left of the number,
we have one, seven, and then five. Since five is the last significant
figure we’re looking for, we round it on the basis of the next digit. The next digit is six, which is
greater than five, so five rounds up to six. So to three significant figures,
the charge-to-mass ratio of an electron is negative 1.76 times 10 to the 11th
coulombs per kilogram. Note that this answer is negative
because the charge of an electron is negative. Also, if we’d used different units,
we would’ve gotten a very different numerical answer because, for example, in units
of the elementary charge, the charge of an electron is exactly negative one.
