"Comparing Formulas: E=p^2/2m and E=hf

In summary, the formulas E=p^2/2m and E=hf are used to calculate the energy of an object in terms of its momentum and mass, and the energy of a photon in terms of its frequency, respectively. Both formulas are commonly used in physics, but for different applications in classical and quantum mechanics. They are related through Planck's constant, but cannot be used interchangeably due to their different physical principles. Additionally, these formulas have limitations in their application, such as not accounting for relativity or the wave-particle duality of light.
  • #1
alik
6
0
What is the difference between formulas E=p^2/2m and E= hf ?
 
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  • #2
You cannot understand a formula without its context. The first E in reality means: Energy of a non-relativistic, non-interacting, classical particle. The second E refers to the energy of a non-interacting, quantum photon.
 
  • #3
p^2/2m is non-relativistic kinetic energy
E=hf usually means total energy of a photon
 

Related to "Comparing Formulas: E=p^2/2m and E=hf

What is the difference between the formulas E=p^2/2m and E=hf?

The formula E=p^2/2m is used to calculate the energy of an object in terms of its momentum and mass, while the formula E=hf is used to calculate the energy of a photon in terms of its frequency. Essentially, the first formula is used for objects with mass, while the second formula is used for particles without mass, such as photons.

Which formula is more commonly used in physics?

Both formulas are commonly used in physics, but their applications are different. The formula E=p^2/2m is commonly used in classical mechanics, while E=hf is used in quantum mechanics.

How are these formulas related to each other?

These formulas are related to each other through the constant h, which is known as Planck's constant. This constant relates the energy of a photon to its frequency, and it also relates the momentum of an object to its wavelength.

Can these formulas be used interchangeably?

No, these formulas cannot be used interchangeably. They have different applications and are based on different physical principles. Using the wrong formula for a specific scenario can lead to incorrect results.

Are there any limitations to these formulas?

Yes, there are limitations to these formulas. The formula E=p^2/2m is only applicable to objects with mass and does not take into account the effects of relativity. The formula E=hf is also limited in its application, as it does not take into account the wave-particle duality of light and other quantum effects.

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