How Much Kinetic Energy Do Electrons Need to Resolve a 10fm Nucleus?

In summary, to observe small objects, one can measure the diffraction of particles with a de Broglie wavelength approximately equal to the object's size. Using the de Broglie equation and energy-momentum conservation, the required kinetic energy for resolving a nucleus of size 10fm is 1240MeV. There is a possibility that the given answer of 1240MeV is incorrect and the relativistic formula should be used instead due to the large kinetic energy of the electron.
  • #1
blade_090
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Homework Statement


To "obeserve" small objects,one measures the diffraction of the particles whose de Broglie wavelength is approximately equal to the object's size.
Find the kinetic energy(in electron volts) required by the electrons to resolve
c) a nucleus of size 10fm.


Homework Equations


I use the de broglie equation
~ = wavelenth
~= h/(2MeEk)^1/2
the ans i found is 1.50x10^10 eV
and energy-momentum conservation
E2=p2c2+Me2c4
but I can't find the correct answer for it
the ans i found is 124MeV

the real ans given is 1240Mev
is there any way to find it??
 
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  • #2
I get the same answer you do.
 
  • #3
does tat mean something wrong with the ans given??
or i should use relativistic formula since the kinetic energy of electron is larger thn rest energy of electron?
 

What is the de Broglie wavelength?

The de Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle, such as an electron or a photon, based on its momentum. It is named after French physicist Louis de Broglie, who proposed the idea in 1924.

How is the de Broglie wavelength calculated?

The de Broglie wavelength can be calculated using the equation λ = h/mv, where λ is the de Broglie wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity. This equation is based on the wave-particle duality principle, which states that particles can exhibit both wave-like and particle-like behavior.

What is the significance of the de Broglie wavelength?

The de Broglie wavelength is significant because it helps explain the wave-like behavior of particles at the quantum level. It also has practical applications in various fields, such as electron microscopy and particle accelerators, where the de Broglie wavelength is used to determine the resolution and energy of particles.

Can all particles have a de Broglie wavelength?

Yes, according to the de Broglie hypothesis, all particles, regardless of their mass, have a de Broglie wavelength. However, this wavelength is only significant for particles with very small masses, such as electrons, protons, and photons.

How does the de Broglie wavelength relate to the uncertainty principle?

The de Broglie wavelength is closely related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The de Broglie wavelength provides a way to quantify this uncertainty by showing that the more accurately we know the momentum of a particle, the less we know about its position.

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