Most probable radii in hydrogen ?

[khurram usman]

most probable radii in hydrogen...?

i just started studying quantum mechanics in college...i was told that according to quantum theory the most probable radii of 1s 2s and 3s in hydrogen are respectively a 6a and 11a, where a=bohrs radius for 1st shell
sir told me that we get these values by solving equations for probability...something about differentiating it and then putting it equal to 0
can anyone please provide me any link where these equations and hopefully more numerical problems are solved? i googled this but could not find anything understandable...so please provide something for starters
thanks

 

[jfy4]

Yes, just like with everyday functions we play with in calculus, if you want to find an extrema, you have to differentiate the function and set that equal to zero and solve. For the hydrogen atom, it is no different. One uses the probability density function and solves for the most probable radius. One can also solve for the "expectation value" or where one would find the electron in the hydrogen if probed many times. In general these are not the same value. I don't have a link for you, sorry... but this is treated commonly in most intro QM books, like Griffiths.

Good luck.