# Solving E=mc^2: What Units to Use?

• Allojubrious
In summary, when solving for energy with E=mc^2, the units that should be used depend on the size of the system being studied. For a macroscopic system, you would use joules. For a microscopic system, electron volts would be more appropriate.
Allojubrious
When solving with E=mc^2 what units should I use in the answer??
For example: (if I have an object with a mass of 43kg)
E=mc^2
E=(43kg)(299792458m/s)^2
E=3.86464727 × 10^18
Now here's my problem, do I include units of J/kg (joules per kilogram) or eV (electron volts)??
If someone could help me it would be very helpful.

Thanks,
Al

What is the SI unit of energy?

Joules are kg*m2/s2. Since the units you chose for mass and c are kg, m and s, Joules are what you get.

Electron volts would require the mass to be given in ${{eV}\over{c^2}}$, which is common in high energy physics or when you're talking about atomic scale stuff. For example, the rest mass of a proton is $938 \times 10^8 {{eV}\over{c^2}}$. By itself, eV is not an SI unit.

Oh ok so the unit would be J/kg, no?
Or would it just be J, because I read that it might be J/kg, so which one??

Allojubrious said:
E=(43kg)(299792458m/s)^2
E=3.86464727 × 10^18

1. What do you get with you multiply/divide the units together as indicated by your calculation? (Don't do any conversions!)

2. What is a joule (J) in terms of kg, m, and s?

The SI unit of energy is Joule.
eV is a convenient unit of energy in some areas of physics. The relationship between eV and Joule is
1eV = 1.6 x 10^-19 J

Oh alright so the unit would be Joule.

Thanks all,
Al

Last edited:
Either is correct, since joules and electron volts are both units of energy. If you are working with a macroscopic sized system, you probably want to use joules. If you are working with a microscopic system (i.e. single particles) then electron volts are probably more convenient.

Khashishi said:
Either is correct, since joules and electron volts are both units of energy. If you are working with a macroscopic sized system, you probably want to use joules. If you are working with a microscopic system (i.e. single particles) then electron volts are probably more convenient.

Ah ok now that explanation makes a lot of sense thanks.

Al

## 1. What is the significance of E=mc^2?

The equation E=mc^2, also known as the mass-energy equivalence, is a fundamental concept in physics that explains the relationship between mass and energy. It states that mass and energy are interchangeable and can be converted into one another.

## 2. What units should be used when solving E=mc^2?

In order to maintain consistency and accuracy, the units used when solving E=mc^2 should be consistent with those used in the equation. This means that the units for mass (m) should be in kilograms (kg) and the units for energy (E) should be in joules (J).

## 3. Can E=mc^2 be used to solve for any type of energy?

Yes, E=mc^2 can be used to solve for any type of energy as long as the units used for mass and energy are consistent. For example, it can be used to calculate the energy released in a nuclear reaction or the energy stored in a mass.

## 4. How does E=mc^2 relate to the theory of relativity?

E=mc^2 is a key component of Einstein's theory of relativity, which explains the relationship between space, time, and gravity. It demonstrates that mass and energy are not separate entities, but rather different forms of the same thing.

## 5. Are there any other important equations related to E=mc^2?

Yes, there are several other equations that are related to E=mc^2 and are important in understanding the concepts of mass and energy. These include the equations for kinetic energy (KE=1/2mv^2), potential energy (PE=mgh), and total energy (E=KE+PE).

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