Deriving the electron speed from a specified orbital

The speed of the electron in terms of the speed of the light is 0.000000000000000000000000000000000856c.In summary, the speed of the electron in the n = 3 state in the Hydrogen atom can be found using the equation En = -E0(z^2/n^2), where E0 is the energy of the electron. Using the momentum equation, E/c, the momentum can be derived and then used to calculate the speed of the electron, which is 0.000000000000000000000000000000000856 times the speed of light. This relationship is in line with the energy-momentum relation, E=pc, and the negative energy of the
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jason0294
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[Mentor's note: this thread was moved from a non-homework forum, therefore it does not use the normal template for homework questions]

What is the speed of the electron in terms of the speed of the light when it is in the n = 3 state in the Hydrogen atom?

I started with this equation to find the energy En=-E0(z^2/n^2)
From that i used the momentum=E/c and found momentum then derived v from p=mv
The system keeps saying I am wrong, is there anything specific I am missing or maybe an equation i should be using instead?
 
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  • #2
jason0294 said:
What is the speed of the electron in terms of the speed of the light when it is in the n = 3 state in the Hydrogen atom?

I started with this equation to find the energy En=-E0(z^2/n^2)
From that i used the momentum=E/c and found momentum then derived v from p=mv

Read http://en.wikipedia.org/wiki/Energy–momentum_relation

Is E=pc true for an electron?

The total energy of the electron in the Hydogen atom is negative. What do you think, why?

ehild
 

1. How is the electron speed calculated in a specified orbital?

The electron speed in a specified orbital is calculated using the formula v = (Z/n)a2/n2, where Z is the atomic number, n is the principal quantum number, and a is the Bohr radius.

2. What is the significance of the electron speed in orbitals?

The electron speed in orbitals is important because it determines the energy and stability of the electron within the atom. Higher speeds can result in the electron escaping the atom, while lower speeds can lead to the electron falling into the nucleus.

3. Can the electron speed in a specified orbital vary?

Yes, the electron speed in a specified orbital can vary depending on the energy level and position of the electron within the atom. It can also change when the electron absorbs or releases energy.

4. How does the electron speed in an orbital relate to its angular momentum?

The electron speed in an orbital is directly proportional to its angular momentum. This means that as the electron speed increases, so does its angular momentum, and vice versa.

5. Is there a limit to the electron speed in an orbital?

According to the principles of quantum mechanics, there is a maximum speed that an electron can have in an orbital. This is known as the speed of light and is approximately 3x108 meters per second.

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