i have done that and the integral of them is equal to 2pi
but once i do the integral of (exp(-2r/a)dr from 0<r<inifinity
i get a/2
this gives me a final answer of 1/(a^2) and the correct answer is 2/(a^2)
do u know where i am missing the extra factor of 2?
i set it up as
integral of (1/(pi)a^3).(exp(-2r/a)/r^2)dr
but i do not no how to convert this into spherical polar i know that the volume element of spherical polar is (r^2)sin(theta)drd(theta)d(phi) but i don't no how to convert the dr line elemnt into spherical polars
well basically i tried using the method of finding the expectation value of (1/r^2) although i was not ble to get the final answer, i thought about doing the integration using spherical polars, becuase there is a factor of pi that will need to be canceled out, but i still couldn't get the...
The normalised wavefunction for the 1s electron in the hydrogen atom is
ψ=(1/((PI^1/2).a^3/2)).exp(-r/a)
where a is the bohr radius.
What is the mean value of (1/r2) in terms of the Bohr radius a0?
Answer: 2/(a^2)
i have two questions that i am struggling with and i have tried all i can think of with them and i am still not getting the answers correct.
1)Estimate, using the Uncertainty Principle, the kinetic energy of an electron if it were bound in the nucleus.
Answer: ∼ 200 MeV for R ∼ 1 fm...