De Broglie Wavelength Calculation for an Electron with 120 eV Energy

In summary, the de Broglie wavelength of an electron with an energy of 120 eV can be calculated using the equation lambda = h/p, where p is equal to the square root of 2 times the mass of the electron times the energy. This results in a wavelength of 1.1E-10m, which is the quoted answer. However, another equation, E=hf, can only be used if the particle is relativistic and has momentum equal to its energy. Otherwise, the relation between wavelength and frequency changes.
  • #1
bennyq
23
0

Homework Statement


Calculate the de Broglie wavelengths of an electron with energy 120 eV ...

Homework Equations


lambda = h\p where p = sqrt(2*Me*E)

The Attempt at a Solution


E=1.6E-19*120ev..
Then sub into equation and I get 1.1E-10m for the wavelength, which is the answer quoted.

The question that concerns me is why can you not use E=hf, where rearranged gives lambda=(hc/E) which gives
a different answer...
Thanks
 
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  • #2
E=hf is valid if E is the total energy, (E=mc2). The formula p = sqrt(2*Me*E) is valid for speeds much less than c, and E means the kinetic energy.
 
  • #3
ehild said:
E=hf is valid if E is the total energy, (E=mc2).

Note that you can only use this for the de Broglie wavelength the way done in the OP if the particle is relativistic and thus has momentum essentially equal to its energy. In other words, when the velocity is close to c - otherwise the relation between wavelength and frequency changes.
 

What is wave-particle duality?

Wave-particle duality is the concept that particles, such as electrons and photons, can exhibit both wave-like and particle-like behavior. This means that they can behave as both a wave and a particle, depending on the experimental setup.

Who first discovered wave-particle duality?

The concept of wave-particle duality was first proposed by French physicist Louis de Broglie in 1924. He suggested that particles have both wave-like and particle-like properties, which was later confirmed by experiments.

How does wave-particle duality affect our understanding of the universe?

Wave-particle duality challenges our classical understanding of the universe, where particles were thought to behave only as particles and waves as waves. It has led to the development of quantum mechanics, which is essential for understanding the behavior of particles at a microscopic level.

What experiments support the theory of wave-particle duality?

Several experiments have been conducted to support the theory of wave-particle duality. The most famous is the double-slit experiment, where particles behave as waves when passed through two slits, creating an interference pattern. Other experiments include the photoelectric effect and the Davisson-Germer experiment.

Can we observe both the wave and particle nature of a particle at the same time?

No, we cannot observe both the wave and particle nature of a particle at the same time. This is known as the principle of complementarity, which states that a particle's wave and particle nature are complementary and cannot be observed simultaneously.

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