The Brogile wavelength of an Alpha particle

In summary: So the correct equation to use is lamda = h/mvIn summary, to calculate the de Broglie wavelength of an alpha particle with an energy of 5.78 MeV, the equation lamda = h/mv should be used, where h is Planck's constant, m is the mass of the alpha particle, and v is its velocity. This wavelength can then be compared to the known nuclear diameter of approximately 2x10^-14 m.
  • #1
mrausum
45
0

Homework Statement



An alpha particle of energy 5.78 MeV is emitted from a particular nucleus.
Calculate the de Broglie wavelength of the alpha particle. How does it compare
with the nuclear diameter, which is known to be approximately 2x10−14 m.


Homework Equations



E=h/p and E=hf

The Attempt at a Solution



I was thinking of using E=hc/lamda but this would be wrong because alpha particles don't travel at c.
 
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  • #2
The energy of 5.78MeV is entirely kinetic.
 
  • #3
so how do i do the question?
 
  • #4
mrausum said:
so how do i do the question?

Use Ek=1/2mv2
 
  • #5
well it hasn't given the mass. But are you saying work out v from E=1/2mv^2, then f from E/h. Then wavelength from lamda=v/f?
 
  • #6
mrausum said:
well it hasn't given the mass. But are you saying work out v from E=1/2mv^2, then f from E/h. Then wavelength from lamda=v/f?

find v, then use

[tex]\lambda = \frac{h}{mv}[/tex]

I am sure you can look up the mass of an alpha particle. I am not sure how else you can solve this problem without my suggestion though.
 
  • #7
how do you get lambda = h/mv
i know E = hc/lambda = h/mv
so, if i combine both equations, shouldn't i suppose to get lambda = cmv ?
did i miss something or what.
 
  • #8
HjGanap said:
how do you get lambda = h/mv
i know E = hc/lambda = h/mv
so, if i combine both equations, shouldn't i suppose to get lambda = cmv ?
did i miss something or what.

p = h/lamda
lamda = h/p=h/mv

You can't use E = hc/lamda because alpha particles don't travel at the speed of light.
 

Related to The Brogile wavelength of an Alpha particle

1. What is the Brogile wavelength of an Alpha particle?

The Brogile wavelength of an Alpha particle refers to the wavelength of the particle when it is in motion. It is determined by dividing the Planck's constant by the momentum of the particle.

2. How is the Brogile wavelength of an Alpha particle calculated?

The Brogile wavelength of an Alpha particle 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.

3. What is the significance of the Brogile wavelength of an Alpha particle?

The Brogile wavelength of an Alpha particle is significant because it shows the wave-like behavior of particles at the atomic level. It also helps in understanding the behavior and properties of particles at the quantum level.

4. How does the Brogile wavelength of an Alpha particle relate to its energy?

The Brogile wavelength and energy of an Alpha particle are inversely proportional. This means that as the wavelength decreases, the energy of the particle increases and vice versa.

5. Can the Brogile wavelength of an Alpha particle be observed?

No, the Brogile wavelength of an Alpha particle cannot be observed directly as it is too small to be detected by any instrument. However, its effects can be observed through various experiments and calculations.

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