De-Broglie Wavelength of a captured electron?

In summary, the de Broglie wavelength of an electron can be found by calculating its energy, momentum, and using conservation of energy and basic kinematic equations. It is also helpful to consider when a neutron and neutrino have the smallest possible energy, which can be approximated to calculate the de Broglie wavelength.
  • #1
Sritika
3
1
For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the
electron must have some minimum energy. For such an electron,how can the de-Broglie wavelength be found out?
 
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  • #2
Calculate the electron energy, calculate its momentum, calculate its de Broglie wavelength.

Is this a homework question?
 
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Likes Sritika
  • #3
mfb said:
Calculate the electron energy, calculate its momentum, calculate its de Broglie wavelength.

Is this a homework question?
Nope.I just came across this question.It kind of intrigued me.With such a minimal information,how can you find out the wavelength?
 
  • #4
Sritika said:
With such a minimal information,how can you find out the wavelength?
With the steps I described.
Conservation of energy and a few basic kinematic equations.
 
  • #5
Hint: under what circumstances does a neutron + neutrino have the smallest possible energy?

(to a very good approximation, at least)
 
  • #6
jtbell said:
Hint: under what circumstances does a neutron + neutrino have the smallest possible energy?

(to a very good approximation, at least)
Please the answer?
 
  • #7
Sritika said:
Please the answer?

When is this [itex]e p \rightarrow n \nu_e[/itex] possible?
 

1. What is the De-Broglie Wavelength of a captured electron?

The De-Broglie Wavelength of a captured electron is a physical property that describes the wave-like behavior of an electron when it is confined to a small space, such as an atom or molecule. It is named after French physicist Louis de Broglie, who proposed the concept of wave-particle duality.

2. How is the De-Broglie Wavelength calculated?

The De-Broglie Wavelength is calculated by dividing the Planck's constant by the momentum of the electron. This can be represented by the equation λ = h / p, where λ is the De-Broglie Wavelength, h is Planck's constant (6.626 x 10^-34 J*s), and p is the momentum of the electron.

3. What is the significance of the De-Broglie Wavelength in atomic systems?

The De-Broglie Wavelength is significant in atomic systems because it helps us understand the behavior of electrons in confined spaces. It also provides a way to describe the quantized energy levels of electrons in atoms, which is important in understanding atomic structure and chemical bonding.

4. Can the De-Broglie Wavelength of a captured electron be measured?

Yes, the De-Broglie Wavelength of a captured electron can be measured using various experimental techniques, such as electron diffraction or scanning tunneling microscopy. These techniques allow us to observe the wave-like behavior of electrons and determine their corresponding De-Broglie Wavelength.

5. How does the De-Broglie Wavelength of a captured electron relate to its speed?

The De-Broglie Wavelength and speed of a captured electron are inversely proportional. This means that as the speed of the electron increases, its De-Broglie Wavelength decreases. This relationship is described by the equation λ = h / mv, where m is the mass of the electron and v is its velocity.

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