Finding the probability of an electron

In summary, the conversation discusses determining the probability of finding an electron in the toroidal region using the psi 320 wavefunction, with the use of cos (theta)=+/- sqrt 1/3 and the integration of the radial part. The conversation also considers the possibility of the wavefunction being negative and the importance of examining the functional form when determining probability.
  • #1
apott155
4
0

Homework Statement



Determine the probability of finding the electron in the region for which the psi 320 wavefunction is negative(toroidal region).

Homework Equations





The Attempt at a Solution


cos (theta)=+/- sqrt 1/3

radial part integrated= r^6*e^(-2r/3a)

Angular part= (9cos(theta)^4-6cos(theta)^2+1)sin(theta)
 
Physics news on Phys.org
  • #2
Can you use the roots cos (theta)=+/- sqrt 1/3 to determine a range of [tex]\theta[/tex] for which the angular part of the wavefunction is negative?
 
  • #3
YUp.
 
  • #4
I tried that, but I don't see where the radial part comes in
 
  • #5
Can the radial part of the wavefunction ever be negative? Note that the quantities you wrote down are the squares of the relevant factors of the wavefunction. (they're also not normalized).
 
  • #6
I don't think so... The ending value has to be inbetween 0 and 1 because its probability
 
  • #7
apott155 said:
I don't think so... The ending value has to be inbetween 0 and 1 because its probability

Be careful. [tex]|\Psi|^2[/tex] is positive and bounded, but [tex]\Psi[/tex] itself isn't so restricted. In this case you need to examine the functional form.
 

1. What is the probability of an electron being in a specific location?

The probability of an electron being in a specific location is described by its wave function, which is a mathematical representation of the electron's probability density. This probability density is not a fixed value, but rather a range of possible values that encompass the electron's position in space.

2. How is the probability of an electron calculated?

The probability of an electron is calculated using the Schrodinger equation, which takes into account the electron's wave function, the potential energy of its surroundings, and other factors such as spin and angular momentum. This equation allows us to determine the probability of finding an electron in a specific location at a given time.

3. Can the probability of an electron be 100%?

No, the probability of an electron being in a specific location can never be 100%. This is because of the inherent uncertainty in quantum mechanics, which states that we can only know either the position or the momentum of a particle with a certain level of accuracy, but never both at the same time.

4. How does the probability of an electron change over time?

The probability of an electron changes over time as its wave function evolves. This evolution is governed by the Schrodinger equation, which takes into account the changes in the electron's surroundings and other factors such as interactions with other particles. As the electron's wave function changes, so does its probability of being in a specific location.

5. Can the probability of an electron be visualized?

While the probability of an electron cannot be directly observed or visualized, it can be represented graphically through its wave function. This allows scientists to understand the likelihood of finding an electron in different regions of space and how it changes over time. However, it is important to note that the wave function itself is not a physical representation of the electron, but rather a mathematical tool used to describe its behavior.

Similar threads

  • Advanced Physics Homework Help
Replies
7
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
764
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
721
Replies
16
Views
553
  • Advanced Physics Homework Help
Replies
1
Views
923
  • Advanced Physics Homework Help
Replies
5
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
854
  • Advanced Physics Homework Help
Replies
21
Views
1K
  • Advanced Physics Homework Help
Replies
10
Views
2K
Back
Top