Radial postion - momentum uncertain for 2s Hydrogen

[TheRascalKing]

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?

 

[DrClaude]

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 $\langle r \rangle$?

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 $k$?

EDIT: would <p> = 0 since Hydrogen 2s is spherically symmetric?

No.