Probability of finding electron.

In summary, the picture shows the first few hydrogen atom orbitals, which are cross-sections of the probability density that are color-coded. The s orbital electrons have the highest probability density in the nucleus, meaning that the probability of finding the electron at a certain distance from the nucleus is highest at r=0. However, the expectation value of the electron's position may not be at the nucleus. Additionally, the radial distribution of s orbitals shows that the probability of finding the electron at a certain distance from the nucleus goes through a maximum away from the nucleus.
  • #1
nil1996
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HAtomOrbitals.png


The picture shows the first few hydrogen atom orbitals (energy eigenfunctions). These are cross-sections of the probability density that are color-coded (black=zero density, white=highest density).according to the picture -Do s orbital electrons have highest probability density in the nucleus?

(i am totally new to quantum mechanics.So please tell if i am wrong.)
 
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  • #2
If you take the radial part of the wave function only, then yes, the probability density ##|\psi|^2## is maximum at ##r=0## for s electrons. But that doesn't mean that the expectation value ##\langle r \rangle## is 0. A measurement will most likely find the electron at a certain distance from the nucleus.

Another way to see it is to consider the radial distribution too. As s orbitals are spherical, the surface of the sphere increases as ##r## increases, so the probability of finding the electron at a certain distance of the nucleus goes through a maximum away from the nucleus.
 

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

The probability of finding an electron in a specific location is determined by its wave function, which describes the probability amplitude of the electron being at a particular point in space. The square of the wave function is equal to the probability density, which gives the likelihood of finding the electron at a certain point.

2. How is the probability of finding an electron related to its energy level?

The probability of finding an electron is directly related to its energy level. The higher the energy level, the larger the area in which the electron is likely to be found. This is because electrons with higher energy levels have a larger wave function, meaning there is a higher probability of finding them in a larger area.

3. What factors affect the probability of finding an electron?

The probability of finding an electron is affected by several factors, including the electron's energy level, the shape and size of the atom or molecule it is in, and the presence of any external electric or magnetic fields. Additionally, the uncertainty principle states that the more precisely we know the position of an electron, the less we know about its momentum, and vice versa.

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

No, the probability of finding an electron in a specific location can never be 100%. This is because of the uncertainty principle, which states that it is impossible to know the exact position and momentum of a particle simultaneously. Therefore, there will always be some uncertainty in the exact location of an electron, no matter how small.

5. How do scientists use the probability of finding an electron in their research?

Scientists use the probability of finding an electron in many different ways, depending on their field of study. For example, chemists use the probability of finding an electron to determine the chemical properties of elements and molecules. In physics, the probability of finding an electron can be used to predict the behavior of particles in quantum systems and to understand the properties of materials. In general, the probability of finding an electron is a fundamental concept in many scientific fields and is essential for understanding the behavior of matter at the atomic and subatomic level.

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