Can an electron in an s-orbital exist at the nucleus (r=0)?

In summary, the probability of finding an electron in a 1s orbital between r and r+dr, according to the quantum textbook, is given by Prob = (4/a^3)*(r^2)*exp(-2r/a) dr. However, due to the r^2 in the volume element, Prob(0) = 0 and it may seem impossible to find an electron at r = 0. However, the volume element at r = 0 is actually 0, but the nucleus is larger than that and therefore has a non-zero volume element, making it possible to find an electron at r = 0. This may contradict what is taught in chemistry classes, but the concept of volume element explains this difference
  • #1
Steven Hanna
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My quantum textbook says that the probability of finding an electron in a 1s orbital between r and r+dr is given by Prob = (4/a^3)*(r^2)*exp(-2r/a) dr. In this case, Prob(0) = 0 because of the r^2, which is part of the volume element in spherical polar. Does this mean that it is impossible to find an electron at r = 0? I have learned the opposite in several chemistry classes, so I would very much appreciate if someone could clear this up.
Thanks!
 
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  • #2
The volume element at r = exactly zero is 0. The nucleus is somewhat bigger than that, and its volume element is non-zero, and therefore so is the probability.
 
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Vanadium 50 said:
The volume element at r = exactly zero is 0. The nucleus is somewhat bigger than that, and its volume element is non-zero, and therefore so is the probability.
Ah of course. Thank you!
 

FAQ: Can an electron in an s-orbital exist at the nucleus (r=0)?

1. Can an electron in an s-orbital exist at the nucleus (r=0)?

No, according to the Schrödinger equation, the probability of finding an electron at the nucleus is zero. This is because the wave function of an s-orbital has a node at the nucleus, meaning there is zero probability of finding an electron at that point.

2. Why is it impossible for an electron in an s-orbital to exist at the nucleus?

This is due to the Heisenberg uncertainty principle, which states that the position and momentum of a particle cannot be simultaneously known with certainty. As the electron moves closer to the nucleus, its momentum increases and its position becomes more uncertain, making it impossible for it to exist at the exact point of the nucleus.

3. Is there any scenario where an electron in an s-orbital could exist at the nucleus?

No, the laws of quantum mechanics do not allow for an electron to exist at the nucleus. Even in extreme conditions such as high pressure or temperature, the electron's wave function will still have a node at the nucleus, preventing it from being located at that point.

4. Can an electron in an s-orbital ever come into contact with the nucleus?

No, the concept of "contact" does not apply at the atomic scale. The electron and nucleus are both quantum objects and do not have a well-defined position or size. They are described by wave functions which can overlap, but never truly touch.

5. How does the probability of finding an electron in an s-orbital change as the distance from the nucleus increases?

The probability of finding an electron in an s-orbital decreases as the distance from the nucleus increases. This is because the wave function spreads out and the electron is less likely to be found in any specific location. However, there is still a non-zero probability of finding the electron at any distance from the nucleus.

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