Probability of finding an electron

In summary, the probability of finding an electron on the z-axis is zero, as the z-axis has no volume. This is in line with the general principle that the probability of a continuous random variable having a specific value is always zero. Therefore, your instructor is correct in stating that the probability of finding the electron on the z-axis is zero.
  • #1
physicsmaths1613
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Let us assume that we have an electron belonging to the px orbital. In that case what would be the probability of finding it on the z axis? Would it be zero? My teacher says so, but I think that because we can't predict the boundary where there is 100% possibility of finding an electron, we can't find a point where the probability of finding it is 0. Who is correct?
 
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  • #2
You instructor is correct if I understand your question. The electron wave function is spread over a volume. Any finite volume the electron will have some chance of being found there. [edit: the smaller the volume the smaller the probability] The z-axis has no volume so the probability is zero.
 
  • #3
Paul Colby said:
You instructor is correct if I understand your question. The electron wave function is spread over a volume. Any finite volume the electron will have some chance of being found there. [edit: the smaller the volume the smaller the probability] The z-axis has no volume so the probability is zero.
Does that mean that the probability of finding the electron on the x-axis is 0 too, as it has no volume like the Z axis?
 
  • #4
Yes, written out ##P_{\Delta V}=\int\int\int_{\Delta V} \vert \psi(x)\vert^2 d^3x## if ##\Delta V=0## then ##P=0##.
 
  • #5
This discussion is a special case of an obvious principle. The probability of a random variable, with a continuous distribution, having a specific value, is 0.
 

Related to Probability of finding an electron

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

The probability of finding an electron in a specific location is described by the electron probability density function, which is determined by the electron's wave function. This function gives the likelihood of finding an electron at a specific point in space.

2. How is the probability of finding an electron calculated?

The probability of finding an electron is calculated by taking the square of the electron's wave function. This gives the probability density function, which represents the likelihood of finding the electron at a specific point in space.

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

No, the probability of finding an electron at a specific point in space can never be 100%. This is because of the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty.

4. How does the probability of finding an electron change in different energy levels?

The probability of finding an electron changes in different energy levels due to the different shapes and sizes of the electron's wave function. In higher energy levels, the electron's wave function is more spread out, resulting in a lower probability of finding the electron at a specific point in space.

5. How does the probability of finding an electron differ in different elements?

The probability of finding an electron differs in different elements due to the different number of protons in the nucleus. This affects the strength of the electron's attraction to the nucleus and the shape of its wave function, resulting in varying probabilities of finding the electron in different elements.

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