- #1

- 41

- 0

So the energy is sometimes calculated like this:

(1)[tex]E= \frac{mv^2}{2}[/tex]

and sometimes like this

(2)[tex]E = mc^2 + \frac{mv^2}{2}[/tex]

When should I use

**1**and when should I use

**2**?

Thank you for any help.

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In summary, when dealing with energy conservation in a system, we can use the simplified equation E=mv^2/2 if the particles in the system are preserving their rest mass. Otherwise, we need to use the more complex equation E=mc^2+mv^2/2. This is why classical theory works for low velocity cases, where the particles have a negligible change in their rest mass.

- #1

- 41

- 0

So the energy is sometimes calculated like this:

(1)[tex]E= \frac{mv^2}{2}[/tex]

and sometimes like this

(2)[tex]E = mc^2 + \frac{mv^2}{2}[/tex]

When should I use

Thank you for any help.

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- #2

Staff Emeritus

Science Advisor

Gold Member

- 2,960

- 4

[tex]E=\gamma mc^2[/tex]

where [tex]\gamma[/tex] is the Lorentz factor:

[tex]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

In the limit of small v, the first equation goes to your second one:

[tex]E=mc^2+\frac{1}{2}mv^2[/tex]

Now, if we have some hypothetical set of particles and we want to conserve total energy, we can write:

[tex]\sum_{i=1}^{N}E_{i,1}=E_x+\sum_{i=1}^{N}E_{i,2}[/tex]

where E

[tex]\sum_{i=1}^{N}(m_{i,1}c^2+\frac{1}{2}m_{i,1}v_{i,1}^2)=E_x+\sum_{i=1}^{N}(m_{i,2}c^2+\frac{1}{2}m_{i,2}v_{i,2}^2)[/tex]

If, for all particles:

[tex]m_{i,1}=m_{i,2}[/tex]

then the equation simplifies to

[tex]\sum_{i=1}^{N}\frac{1}{2}m_{i,1}v_{i,1}^2=E_x+\sum_{i=1}^{N}\frac{1}{2}m_{i,2}v_{i,2}^2[/tex]

because the mc

In words, as long as the components of your system are preserving their rest mass, then the mc

- #3

- 1,466

- 1

The equation (1) is known as the classical kinetic energy formula and is used to calculate the kinetic energy of an object with mass m and velocity v. This equation is applicable for objects moving at speeds much slower than the speed of light.

On the other hand, equation (2) is known as the relativistic energy formula and takes into account the effects of special relativity at high speeds. This equation is applicable for objects moving at speeds close to the speed of light, such as electrons.

Therefore, if you are dealing with an electron moving at a speed close to the speed of light, it is more accurate to use equation (2) to calculate its energy. However, if the electron is moving at a much slower speed, equation (1) will provide a good approximation.

It is important to note that both equations are valid and can be used depending on the context of the problem. It is always best to use the appropriate equation based on the speed of the electron in order to obtain a more accurate result.

The formula for calculating the energy of an electron is E = -13.6/n^2, where n is the number of the energy level.

The unit of measurement for the energy of an electron is electron volts (eV).

The energy of an electron is related to its position in an atom by its energy level. Electrons with higher energy levels are farther from the nucleus and have more energy.

Calculating the energy of an electron is important because it helps us understand the behavior and properties of atoms and molecules. It also allows us to predict the chemical reactivity of elements and compounds.

Yes, the energy of an electron can be negative. This simply means that the electron has less energy than a free electron at rest, which is defined as having an energy of 0 eV.

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