Radial postion - momentum uncertain for 2s Hydrogen

In summary, the individual is seeking help with calculating delta r * delta p for the hydrogen atom in the 2s state. They have provided equations and attempted to calculate the expectation values for <r> and <p>, but are unsure if their calculations are correct. They also question whether the expectation value for <p> would be 0 due to the spherically symmetric nature of the 2s state.
  • #1
TheRascalKing
7
0

Homework Statement


I'm trying to calculate delta r * delta p for the Hydrogen atom in the 2s state

Homework Equations


ψ(r) = (1/ 2√π) (1 / 2a)^(3/2) (2 - (r/a)) e^(-r/2a)
where a is the bohr radius

The Attempt at a Solution


I figured out that <r> = 6a, but I'm at a loss as to how to figure out <r2> or <p>.

Using E = (-ke2 / 2a)(1/n2), and p2 = 2mE, i found <p2> = (m/2)(-ke2 / 2a), but I am not 100% sure this is right

EDIT: would <p> = 0 since Hydrogen 2s is spherically symmetric?
 
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  • #2
TheRascalKing said:
I figured out that <r> = 6a, but I'm at a loss as to how to figure out <r2> or <p>.
How did you calculate ##\langle r \rangle##?


TheRascalKing said:
Using E = (-ke2 / 2a)(1/n2), and p2 = 2mE, i found <p2> = (m/2)(-ke2 / 2a), but I am not 100% sure this is right
What is ##k##?

TheRascalKing said:
EDIT: would <p> = 0 since Hydrogen 2s is spherically symmetric?
No.
 

Related to Radial postion - momentum uncertain for 2s Hydrogen

1. What is radial position and momentum uncertainty in the context of 2s Hydrogen?

Radial position and momentum uncertainty in 2s Hydrogen refer to the uncertainty in the location and momentum of the electron in the hydrogen atom's second energy level. This uncertainty is a fundamental aspect of quantum mechanics, where the exact position and momentum of a particle cannot be simultaneously known.

2. How is radial position and momentum uncertainty calculated for 2s Hydrogen?

Radial position and momentum uncertainty in 2s Hydrogen can be calculated using the Heisenberg uncertainty principle, which states that the product of the uncertainties in position and momentum must be greater than or equal to a constant value. In the case of 2s Hydrogen, this constant is equal to Planck's constant divided by 4π.

3. What factors affect the radial position and momentum uncertainty in 2s Hydrogen?

The radial position and momentum uncertainty in 2s Hydrogen are affected by the energy level of the electron, as well as the mass and charge of the nucleus. The uncertainty also increases as the size of the atom increases, since the electron's position becomes less localized.

4. How does radial position and momentum uncertainty in 2s Hydrogen relate to other quantum mechanical principles?

The uncertainty in the electron's position and momentum in 2s Hydrogen is related to other principles, such as the wave-particle duality and the quantization of energy levels. This uncertainty is a fundamental aspect of quantum mechanics and is essential for explaining the behavior of atoms and subatomic particles.

5. Can the radial position and momentum uncertainty of 2s Hydrogen be reduced or eliminated?

No, the uncertainty in the radial position and momentum of 2s Hydrogen cannot be reduced or eliminated. This uncertainty is a fundamental aspect of quantum mechanics and is a result of the probabilistic nature of subatomic particles. However, the uncertainty can be minimized by decreasing the energy level of the electron, but it cannot be completely eliminated.

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