Video Transcript
Which of the following relations is
correct? (A) To convert an amount of energy
from joules to mega-electron volts, we divide it by 1.6 times 10 to the negative
27. (B) To convert an amount of energy
from joules to mega-electron volts, we divide it by 1.6 times 10 to the negative
13. (C) To convert an amount of energy
from joules to mega-electron volts, we multiply it by 1.6 times 10 to the negative
27. (D) To convert an amount of energy
from joules to mega-electron volts, we multiply it by 1.6 times 10 to the negative
13.
An electron volt is the amount of
energy gained by an electron when it travels through a potential of one volt. This unit of energy is commonly
used for energy changes in atomic processes. For example, removing the electron
from a hydrogen atom requires 13.6 electron volts of energy. Breaking apart the helium nucleus
into protons and neutrons requires 28.3 mega-electron volts of energy. Mega-electron volts are the subject
of this question. We need to determine the
relationship between mega-electron volts and joules.
There are one million electron
volts in a mega-electron volt. We can also express one million as
10 to the sixth. So we can convert from
mega-electron volts to electron volts if we multiply by 10 raised to the power of
six. One electron volt is equivalent to
1.602 times 10 to the negative 19 joules. So we can convert from electron
volts to joules if we multiply by this number. The combination of these two
conversions gives us 1.602 times 10 to the negative 13 joules, which we’ll round to
one decimal place to match the answer choices. So one mega-electron volt is equal
to 1.6 times 10 to the negative 13 joules.
We can rule out answer choices (A)
and (C) as our conversion factor is not 1.6 times 10 to the negative 27. Now we need to know if we should
divide or multiply by this number. So if we had some amount of energy
in joules and we want to convert it into mega-electron volts, we would divide by our
conversion factor. We can see this way that the units
of joules cancel, leaving us in the correct units of mega-electron volts. So of the relations in this
problem, answer choice (B) was correct. To convert an amount of energy from
joules to mega-electron volts, we divide it by 1.6 times 10 to the negative 13.
