Electron Capture by alpha particle -- Frequency of photon?

In summary: The energy of the photon is the difference of the two states. Subtracting a negative value from a positive will lead to an answer that is larger than the positive value. In other words, your photon will have an energy of more than 50 eV.
  • #1
NucEngMajor
21
0

Homework Statement


Electron with KE = 50eV is captured by Alpha particle, ie. HE++. Calculate the frequency of the emitted photon.

Homework Equations


KE = m/2 v^2; E=hf, En = Z^2*-13.6eV/n^2

The Attempt at a Solution


Energy before = Energy after
50eV = 4*-13.6eV/1 + hf
f = 1200nm
 
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  • #2
Something went wrong between the last two lines, the wavelength is way too long.
Also, 1200 nm is a length, not a frequency.

The electron doesn't have to go to the ground state directly, so you should at least say that you assume this.
 
  • #3
Right. I solved for wavelength. 50 eV is a big KE so 1200nm seems reasonable? In general is the conservation of energy correct? I mean is it appropriate to put En + hf rather than Potential + hf?
 
  • #4
The approach is right, just the result is wrong.
1200 nm is infrared light, with an energy of about 1 eV per photon. And 1200 nm is not a frequency, the problem statement asks for the frequency.
 
  • #5
mfb said:
The approach is right, just the result is wrong.
1200 nm is infrared light, with an energy of about 1 eV per photon. And 1200 nm is not a frequency, the problem statement asks for the frequency.
Would you kindly explain why its T = En + hf and NOT T = U(r) + hf?
 
  • #6
What is U(r)?
That looks like a very classical approach.
 
  • #7
mfb said:
What is U(r)?
That looks like a very classical approach.
I'm just confused why the energy is En plus some additional hf. Initially it is unbound, n = infinity, right? After we drop to some E1 or En?
 
  • #8
NucEngMajor said:
Initially it is unbound, n = infinity, right?
It is unbound with its energy above zero, so "n=infinity" is a problematic concept.

Initially it is unbound and has a positive energy, afterwards it is bound and has a negative energy. The energy of the photon is the difference of the two states. Subtracting a negative value from a positive will lead to an answer that is larger than the positive value. In other words, your photon will have an energy of more than 50 eV.
 

1. What is electron capture by alpha particle?

Electron capture by alpha particle is a type of nuclear reaction in which an unstable atomic nucleus captures an orbiting electron, resulting in the formation of a more stable nucleus.

2. How does electron capture by alpha particle occur?

During electron capture, an alpha particle (a helium nucleus) approaches the unstable atomic nucleus and combines with one of its orbiting electrons. This results in the formation of a new element with a lower atomic number.

3. What is the frequency of photon in electron capture by alpha particle?

The frequency of photon in electron capture by alpha particle varies depending on the specific elements involved in the reaction. It is typically in the form of gamma rays, which have high frequencies and short wavelengths.

4. What is the significance of electron capture by alpha particle?

Electron capture by alpha particle is an important process in nuclear physics, as it can lead to the formation of stable nuclei and also affects the stability of certain elements. It is also used in medical imaging techniques, such as PET scans.

5. How is electron capture by alpha particle studied in the laboratory?

Scientists study electron capture by alpha particle by conducting experiments with radioactive elements and measuring the resulting changes in the atomic structure. This allows for a better understanding of nuclear reactions and the properties of different elements.

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