## De Broglie equation

$\lambda=\frac{h}{p}$

Chloe Qiao 4C
Posts: 65
Joined: Fri Sep 28, 2018 12:27 am

### De Broglie equation

Can someone explain how De Broglie equation is derived? I have on my notebook that energy is equal to momentum times velocity but I really do not understand this and could not go on.

Megan Gianna Uy 3L
Posts: 30
Joined: Fri Sep 28, 2018 12:26 am

### Re: De Broglie equation

c=(lambda)(frequency) and E=h(frequency)
Therefore, E=(hc)/lambda
ALSO, E=mc^2, where m*c=p, so E=pc
Thus, pc=(hc)/lambda,
Therefore, lambda=h/p, and p=momentum(m*v)
So, lambda=h/(m*v)

Nicholas Kull_3L
Posts: 30
Joined: Fri Sep 28, 2018 12:23 am

### Re: De Broglie equation

The equation for the speed of light is c= (lambda) x (v frequency). Momentum (p) = (mass, m) x (velocity, v), E = pc, and E = hv are the base equations needed to find De Broglie's equation. In the equation E = hv, v is the frequency and is equal to c/lambda after rearranging the speed of light equation. Now, we can set the two equations that have (E =) equal to each other so that pc = hc/lambda. Next, both c's cancel each other out leaving you with the equation p = h/lambda. Lastly, set the equation equal to lambda resulting in De Broglie's equation of h/p = lambda.

Vy Lu 2B
Posts: 59
Joined: Fri Sep 28, 2018 12:24 am

### Re: De Broglie equation

To derive the de Broglie equation, we rely on these equations:
c (speed of light) = (lambda, wavelength)(nu, frequency)
E (energy) = (momentum)(velocity)

Note that for a photon, E = (momentum)(speed of light, c) because the velocity of a photon is the speed of light and E = (h, planck's constant)(nu, frequency).

Manipulate c (speed of light) = (lambda, wavelength)(nu, frequency) with respect to frequency: (nu, frequency) = c (speed of light)/(lambda, wavelength).
Manipulate E = (h, planck's constant)(nu, frequency) by plugging in the previous manipulated function into place of nu.

Now equate this E = (momentum)(speed of light, c) to the manipulated equation to get (momentum)(speed of light, c) = (h, planck's constant)(Speed of light, c)/(lambda, wavelength).
Solve for wavelength and you will get the de Broglie equation.