Where is the Classically Forbidden Region for a Ground-State Hydrogen Atom?

[Shafikae]

Any region of space in which the kinetic energy T of a particle would become negative is forbidden for classical motion. For a hydrogen atom in the ground state:
(a) find the classically forbidden region
(b) using the ground-state wave function $$\psi$$₁₀₀(r), calculate the probability of finding the electron in this region.

I was able to do part (b) and I got 0.238103.
As for part (a), I don't know what to do. I'm able to do the mathematics, I just can't seem to start a problem. Thank you.

 

[grey_earl]

Ehhmmm, but if you have calculated the probability of finding the electron in the classically forbidden region, you already must know what this region is, right?
(and yes, you could have added that to your other post. helps keeping an overview)

 

[vela]

I think your answer to part (b) is wrong as well.

 

[Shafikae]

Oh you grey earl... totally forgot 1-P ...
Vela so part (b) is incorrect? This is how I got the answer...

Since a₀ = bohr radius
then the prob of the electron being found in classically forbidden region is (r>2a₀)

Then I took the integral of r² exp(-2r/a₀) (4/a₀) from 2a₀ to infinity... is that not right?

 

[vela]

That's the right method (though I think you meant you had a₀³ in the denominator). I must have screwed up somewhere in my calculation yesterday. Today, I redid it and got the same answer you did. Sorry to mislead you.

 

[Shafikae]

ya sorry i meant cubed. ok good good so I'm on the right track. Thanks so much.

 

[Shafikae]

for part (a), i know i would subtract part (b) from 1... but i want to do that actual math.
Does the integral remain the same and just change the limit of integration from 0 to a₀ ?

 

[vela]

I think you're misunderstanding what the problem is asking for. It's just asking where in space would the electron never be found classically. You've already figured that out (and used it to calculate the answer to part (b)). You wouldn't find it anywhere farther away than 2a₀ from the nucleus; in other words, the classically forbidden region is r>2a₀.

 

[Shafikae]

ohhhhhhhhhhhhhhhhhhhhh! I don't know why i thought number 1 was asking for something totally different! thanks a bunch!

 

[Shafikae]

I thought part (a) was asking for the prob of not finding it in the forbidden region.