# Argh - De Broglie and the wave equation

• B1ueguy1
In summary, the de broglie equation for light states that the wavelength is inversely proportional to the speed of light. For electrons, this equation is not valid because they have no rest mass.
B1ueguy1
This isn't a homework question, but something which has been bugging me. I can't figure it out. Maybe it's late, but it's probably a very stupid question

If light shines onto a denser medium, the light slows down in this medium right? If the light slows down, then by the wave equation, v = fλ, since f is constant, the wavelength must decrease.

So why is it that de broglie's equation λ = h/mv implies a decrease in velocity would increase the wavelength?

I'm so confused...

v is in the denominator

qwerty2x said:
v is in the denominator

eh?

de broglie: λ = h/mv
wave equation: λ = v/f

if anyone has any insight, could someone please help me? It's sort of urgent. I'm taking an exam tomorrow and this uncertainty is really making me nervous.

Well... the de broglie equation is $$\lambda=\frac{h}{p}$$. I don't really think that $$p=mv$$ works for light, because photons have no mass.

I don't really know what I'm talking about though.

B1ueguy1 said:
This isn't a homework question, but something which has been bugging me. I can't figure it out. Maybe it's late, but it's probably a very stupid question

If light shines onto a denser medium, the light slows down in this medium right? If the light slows down, then by the wave equation, v = fλ, since f is constant, the wavelength must decrease.

So why is it that de broglie's equation λ = h/mv implies a decrease in velocity would increase the wavelength?

I'm so confused...

The equation $$p=mv$$ does not hold for photons (light quanta) since they have no rest mass. For a photon, its energy, $$E=h \nu$$ (Planck's constant multiplied by frequency) is equal to its momentum multiplied by the speed of light in vacuum (Generally, for relativistic motion, $$E^{2}=(pc)^{2}+(mc^{2})^{2}$$; Since m is zero in the case of the photon $$E=pc$$. In this case, de Broglie's equation becomes

$$\lambda = \frac{h}{p}=\frac{hc}{E}=\frac{hc}{h \nu}=\frac{c}{\nu} \Rightarrow \lambda \nu =c$$

americanforest said:
The equation $$p=mv$$ does not hold for photons (light quanta) since they have no rest mass. For a photon, its energy, $$E=h \nu$$ (Planck's constant multiplied by frequency) is equal to its momentum multiplied by the speed of light in vacuum (Generally, for relativistic motion, $$E^{2}=(pc)^{2}+(mc^{2})^{2}$$; Since m is zero in the case of the photon $$E=pc$$. In this case, de Broglie's equation becomes

$$\lambda = \frac{h}{p}=\frac{hc}{E}=\frac{hc}{h \nu}=\frac{c}{\nu} \Rightarrow \lambda \nu =c$$

Thank you! So for electrons use debroglie, for light, use the other..

## 1. What is the De Broglie equation?

The De Broglie equation is a fundamental equation in quantum mechanics that relates the wavelength of a particle to its momentum. It is given by λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.

## 2. Who discovered the De Broglie equation?

The De Broglie equation was discovered by French physicist Louis de Broglie in 1924. His work on the wave-particle duality of matter laid the foundation for modern quantum mechanics.

## 3. How is the De Broglie equation related to the wave-particle duality?

The De Broglie equation is a manifestation of the wave-particle duality of matter, which states that particles can exhibit both wave-like and particle-like behavior. The equation relates the wavelength of a particle (a wave-like property) to its momentum (a particle-like property).

## 4. Can the De Broglie equation be applied to all particles?

Yes, the De Broglie equation can be applied to all particles, including subatomic particles such as electrons, protons, and neutrons, as well as larger particles like atoms and molecules. However, it is most commonly used to describe the behavior of particles at the quantum level.

## 5. What is the significance of the De Broglie equation?

The De Broglie equation is significant because it provides a mathematical framework for understanding the wave-like nature of matter. It also helped to unify the fields of quantum mechanics and classical mechanics, as it showed that particles can exhibit both wave-like and particle-like behavior depending on the circumstances.

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