Quantum mechanics quick question

In summary, the conversation discusses the expectation value of a 2p orbital and where the electron is likely to be found relative to the maximum. The conversation also mentions a formula for the expectation value found on a forum, but the person is looking for a more reliable source. The person also mentions they have an exam the next day and is looking for some clarification before walking out the door. They suggest that the electron is likely to be found under the maximum of the "fat" part of the orbital and where it is thickest. However, they also mention that an orbital is an area of probability and could be found everywhere at once. The question of what the expectation value is for (r, x, y, z) is also raised
  • #1
Radfire
7
0

Homework Statement


Where would the expectation value on a 2p orbital lie? and where would you likely find the electron relative to the maximum?


Homework Equations



found on a forum that the expectation value is n^2 a_0 but id like a more reliable source

The Attempt at a Solution



have an exam in morning and its just something which would be nice to know before i walk out the door.

using the formula gives an idea but I am not sure if that's even a proper formula. if i was to guess id say under the maximum of the "fat" part of the orbital since its an average value. and for the second part I am guessing that to would be where the orbital is thickest, even though i know an orbital is an area of probability so technically it could be everywhere at once in the orbital.
 
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  • #2
Expectation value of what — r, x, y, z?
 
  • #3
question doesn't say, id guessing it means the average position of an electron so maybe take 2p_x and find <x>
 

1. What is quantum mechanics?

Quantum mechanics is a branch of physics that explains the behavior of matter and energy at the smallest scale, such as atoms and particles. It is a fundamental theory that helps us understand the nature of the universe at a microscopic level.

2. How is quantum mechanics different from classical mechanics?

Classical mechanics is based on Newton's laws of motion and describes the behavior of macroscopic objects, while quantum mechanics describes the behavior of subatomic particles. In classical mechanics, objects have definite properties and follow predictable paths, but in quantum mechanics, particles can exist in multiple states and have uncertain positions and velocities.

3. What are the key principles of quantum mechanics?

The key principles of quantum mechanics include superposition, where particles can exist in multiple states at the same time, and entanglement, where particles can become correlated even when separated by large distances. Other principles include uncertainty, where the position and momentum of a particle cannot be known simultaneously, and quantization, where energy and other physical quantities are restricted to discrete values.

4. How is quantum mechanics applied in real-world scenarios?

Quantum mechanics has many applications in modern technology, such as in transistors, lasers, and nuclear power. It is also the basis for many modern technologies, including computers, smartphones, and GPS systems. In addition, it has been used in fields such as chemistry, biology, and materials science to understand and manipulate the behavior of molecules and materials at a molecular level.

5. What are some current theories and debates in quantum mechanics?

Some current theories and debates in quantum mechanics include the interpretation of the wave function, the measurement problem, and the role of consciousness in determining outcomes. Other areas of research include quantum computing and quantum information theory, which explore the potential applications of quantum mechanics in information processing and communication.

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