How many particles have momentum in a specific interval?

In summary, the conversation discusses a pulse containing 1000 α particles and their momenta at t=0. The state of each particle is given by ψ(x,0){1/10e^(-ik_0 ) lxl≤50cm, k_0=π/50 and 0 for elsewhere}. The question asks for the number of particles with momenta in the interval 0<hk<hk_0. The solution involves calculating the expectation value of the probability for a particle to have that momentum.
  • #1
najima
34
0

Homework Statement



a pulse 1 m long contains 1000 α particles.at t=0,each α particles in the state

ψ(x,0){1/10e^(-ik_0 ) lxl≤50cm,k_0=π/50 and 0 for elsewhere,}
at t=0 ,how many particle s have momentume in the interval 0<hk<hk_0?

Homework Equations


introduction to quantum mechanics by liboff chapter 5/problems 4


The Attempt at a Solution

I don't understand what does it mean! I think I have to calculate expectation value?am I right?
 
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  • #2


Expectation value of what? You are asked for the number of particles within a certain range of momenta. Since you know there are 1000 particles it would be sufficient to determine the percentage within that range. Looks to me like you want to calculate the probabilty a given particle has that momentum.
 
  • #3


I can't get the answer ,please, help more.:-(
 
  • #4


oh !finally I got! thax man!
 

1. What are alpha particles?

Alpha particles are a type of ionizing radiation consisting of two protons and two neutrons bound together. They are typically emitted during radioactive decay and have a positive charge.

2. How are alpha particles produced?

Alpha particles are produced through the decay of certain unstable nuclei, such as uranium or radium. These nuclei emit an alpha particle in order to become more stable.

3. What is the pulse of alpha particles?

The pulse of alpha particles refers to the rapid release of energy as they travel through a medium. This energy is emitted in the form of ionization, which can be detected and measured by specialized equipment.

4. How is the pulse of alpha particles measured?

The pulse of alpha particles can be measured using a variety of techniques, including scintillation detectors, ionization chambers, and cloud chambers. These instruments detect the ionization produced by the alpha particles and convert it into a measurable signal.

5. What is the significance of studying the pulse of alpha particles?

Studying the pulse of alpha particles can provide valuable information about the properties and behavior of these particles. This can help in understanding the nature of radioactive decay and its effects on living organisms, as well as in developing new technologies for detecting and measuring radiation.

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