De broglie wavelength and energy

In summary, the potential-energy function U(x) has a constant value U_0 in the interval 0 < x < L and is zero outside this interval. An electron with energy E = 6 U_0 is moving past a square barrier with a height of U_0. The ratio of the de Broglie wavelength of the electron in the region x > L to the wavelength for 0 < x < L is 1/sqrt(6). This can be determined using the equation λ=h/p= h/ sqrt(2mK), where K is the kinetic energy of the electron. The total energy of the electron is conserved and equal to E = 6 U_0 everywhere.
  • #1
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Homework Statement


The potential-energy function U(x) has the constant value U_0 in the interval 0 < x < L and is zero outside this interval. An electron is moving past this square barrier, but the energy of the electron is greater than the barrier height.

If E= 6 U_0, what is the ratio of the de Broglie wavelength of the electron in the region x > L to the wavelength for 0 < x < L?

Homework Equations



λ=h/p= h/ sqrt(2mK)

The Attempt at a Solution



K are for x>L and K are for 0<x<L

lamda1 / lambda 2 = sqrt(K2) / sqrt (K1) = sqrt (U_0) / sqrt (6U_0) = 1/ sqrt(6)

anyone.. please help me to spot the mistakes.. :(
 
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  • #2
K is never equal to Uo.

What is the relation between K, U, and total energy E ?
 
  • #3
redbelly98 said:
k is never equal to uo.

What is the relation between k, u, and total energy e ?

e=k + u
 
  • #4
Okay. So what is K when 0 < x < L ?
 
  • #5
redbelly98 said:
okay. So what is k when 0 < x < l ?

k = e - u_0 = u_0 ?
 
  • #6
marpple said:
k = e - u_0 = u_0 ?

No.

The problem statement says E = ____ ?
 
  • #7
Redbelly98 said:
No.

The problem statement says E = ____ ?

6 U_0

but, then i guess E = 6 U_0 is for K x > L
 
  • #8
E = 6 U_0 is for everywhere, all the time. Total energy is conserved, a constant, and never changes.
 
  • #9
Redbelly98 said:
E = 6 U_0 is for everywhere, all the time. Total energy is conserved, a constant, and never changes.

yup.,, got it..
thanks :)
 

1. What is the De Broglie wavelength?

The De Broglie wavelength is a concept in quantum mechanics that describes the wavelength associated with a particle. It is named after Louis de Broglie, who proposed that all particles have a wavelength, similar to waves of light.

2. How is the De Broglie wavelength calculated?

The De Broglie wavelength can be calculated using the equation 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. This equation is based on the principle that all particles have both wave-like and particle-like properties.

3. What is the relationship between De Broglie wavelength and energy?

The De Broglie wavelength and energy are inversely proportional. This means that as the wavelength decreases, the energy of the particle increases, and vice versa. This relationship is described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

4. How does the De Broglie wavelength relate to the wave-particle duality theory?

The De Broglie wavelength is a key concept in the wave-particle duality theory, which states that all particles have wave-like and particle-like properties. The De Broglie wavelength is a manifestation of this duality, as it shows that particles can have a wavelength just like waves do.

5. What is the significance of the De Broglie wavelength in quantum mechanics?

The De Broglie wavelength is significant in quantum mechanics because it helps to explain and predict the behavior of particles on a microscopic scale. It also provides a deeper understanding of the wave-particle duality theory and has implications in various fields, such as atomic and molecular physics, solid-state physics, and quantum computing.

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