## De Broglie Equation

kevinav
Posts: 32
Joined: Fri Sep 28, 2018 12:16 am

### De Broglie Equation

Where does the De Broglie equation, λ= h/mv, come from? Is it related to the equation for kinetic energy?

Posts: 30
Joined: Fri Sep 28, 2018 12:26 am

### Re: De Broglie Equation

De Broglie first used Einstein's famous equation relating matter and energy:
E=mc^2

Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation:
E=hν

he then set them equal to each other
mc^2=hν

Because real particles do not travel at the speed of light, De Broglie submitted velocity ( v ) for the speed of light ( c ).
mv^2=hν

Through the equation λ , de Broglie substituted v/λ for ν and arrived at the final expression that relates wavelength and particle with speed.
mv^2=hv/λ
Hence
λ=hv/mv^2=h/mv

Ronak Singh
Posts: 31
Joined: Fri Sep 28, 2018 12:16 am

### Re: De Broglie Equation

De Broglie's equation is the relationship between wavelength and objects that have a mass and velocity. It suggests that all objects with momentum can exhibit wavelike properties, although some objects have wavelengths that are currently undetectable.

305154707
Posts: 31
Joined: Fri Sep 28, 2018 12:16 am

### Re: De Broglie Equation

The DeBroglie equation comes from a combination of E=mc^2 and E=hv (v is frequency)

1. Substitute "E" for hv, Planck's theory states " every quantum of a wave has a discrete amount of energy " based on E=hv. Broglie believed particles and waves had the same traits, so he set the two energies equal to each other.
E=mc^2 -----> hv=mc^2

2. DeBroglie didn't think that particles traveled at the speed of light (C). To be more realistic, he replaced c with velocity.

m(velocity)^2= hv

3. Substituting velocity for c in "c=lambda(v)", we find velocity= lambda(v). Solving for frequency(v), we get

v= velocity/lambda

4. Inserting this for frequency(v) in m(velocity)^2=hv, we get

m(velocity)^2= h(velocity)/lambda

5. Now, solving for lambda, we get

lambda= (h)(velocity)/(m)(velocity)^2

6. Cancel out the velocities and you're left with De Broglie's equation

(h)/(m)(velocity)

Hope this helped because I learned a lot too!!