What is eight times 10 to the
negative 19th joules in electron volts?
Okay, so here we have an amount of
energy quoted in the specific unit of joules, and we want to state what that amount
of energy is equivalent to in a different energy unit, electron volts. So we have some set amount of
energy, and we’re changing the way we represent it from joules to electron
volts. To figure out how to make this
conversion, let’s recall how many joules are in one electron volt. If we write out this conversion to
three decimal places, then we can recall that one electron volt is equal to 1.602
times 10 to the negative 19th joules. We want to apply this ratio to this
number right here to remove the unit of joules and replace it with electron
volts. To do that, we can multiply our
energy in joules by this ratio.
Notice two things about it. First, the value we have in our
numerator is equal to the value in our denominator. That’s true based on this equation
over here. So effectively, by multiplying by
this fraction, we’re just multiplying our energy in joules by one. But what this multiplication will
do, and this is the second thing we can notice, is cancel out the unit of joules in
our energy value and replace it with the unit of electron volts. We see that this takes place
because we have a unit of joule in our numerator and in our denominator. And therefore, those units
cancel. So that when we carry out this
multiplication, we’ll be left with a value in units of electron volts.
Entering the expression on our
calculator, we find a result to one significant figure of five electron volts. Now, we keep just one significant
figure because we only had one in our original energy value. We can say then that eight times 10
to the negative 19th joules is equal to five electron volts.