# Determine the most probable radius for a 2s orbital (Hydrogen atom)

1. Nov 21, 2007

### science_1999

1. The problem statement, all variables and given/known data

Determine the most probable radius for a 2s orbital (Hydrogen atom)

2. Relevant equations

Wavefunction for a 2s orbital:

1/(4√2pi*a^(3⁄2) ) (2-r⁄a) e^((-r)⁄(2a)) where, a=bohr radius

3. The attempt at a solution

First step:
find the probability density by squaring the wavefunction and multiplying but the spherical element of Volume

Second step:
Set the derivative of the probability density equal to zero to solve for where the slope of the plotted function is equal to zero

2. Nov 21, 2007

### nrqed

So you know all the steps, you simply have to go ahead!

Are you stuck on something?

3. Oct 7, 2009

### gijoe

i am working on the same problem, and i am stuck on one particular part, when i take the derivative and set it equal to zero i end up with a cubic polynomial, like

(r/a)^3 - 6(r/a)^2 + 8r/a - 4 =0

not sure it this is correct, and if it is then do i need to use a graphing program to calculate the min and max points (roots) or is there an easier way?

thanks in advance for any help...

4. Dec 14, 2010

### Ed Aboud

Stuck on this problem also!!

I get to a stage where I get a massive cubic equation...I'm assuming I've gone wrong somewhere...

Any help? Or any online resources where the problem is worked through...?

5. Dec 14, 2010

### gijoe

think i ended up solving it sometime last year.. think the equation factors to something like: (x-4)*(x-2)*(x-2)=0 or something like that.. roots are then 4 & 2.. cant remember exactly but hope this points you in the right direction.... oh x=r/a) of course..