Video Transcript
How much energy would be produced
if an atom with a mass of two unified atomic mass units was completely converted
into energy? Give your answer to two decimal
places and in units of joules.
To answer this question, we need to
convert a mass value into an energy value. Mass and energy can be related
using Einstein’s equation, which can be written as Δ𝐸 equals Δ𝑚𝑐 squared. Δ𝐸 is the change in energy in
joules, Δ𝑚 is the change in mass in kilograms, and 𝑐 is the speed of light in
meters per second. The speed of light is a constant,
which we can approximate to be three times 10 to the eighth meters per second.
In this question, we’ve been given
the mass of an atom in unified atomic mass units. But in order to use Einstein’s
equation, we need the mass in kilograms. To convert between these two mass
units, we’ll need to use the conversion factor one unified atomic mass unit equals
1.66 times 10 to the negative 27th kilograms. We can convert the two unified
atomic mass units into kilograms by multiplying by the conversion factor written as
a fraction. We’ll need to write the conversion
factor with kilograms in the numerator and unified atomic mass units in the
denominator so that the unified atomic mass units cancel.
Performing the calculation gives us
a mass of 3.32 times 10 to the negative 27th kilograms. Now we can plug the change in mass
and the speed of light into the equation. The speed of light squared is nine
times 10 to the 16th meters squared per second squared. Multiplying the change in mass by
the speed of light squared gives us 2.988 times 10 to the negative 10th kilogram
meters squared per second squared. We’ve converted the mass into
energy, but we need to give our answer in units of joules. As it turns out, the unit kilogram
meters squared per second squared is the same as the unit joule.
Finally, we need to round our
answer to two decimal places. Rounding appropriately, we have
determined that if an atom with a mass of two unified atomic mass units was
completely converted into energy, 2.99 times 10 to the negative 10th joules of
energy would be produced.
