About the unit of Radial wave function R(r) of Hydrogen atom

[caoyuan9642]

The 1s radial function of the wave function of H atom is:

R₁₀=2 a^-3/2e^-r/a

,where a = 5.29*10^-11 meter

but substituting a with its value,we will get

R₁₀ = 5.2*10¹⁵ *e^{(-1.89036*1010 r)}
and that is impossible if r=a and R(r)=1.9*10¹⁵

where is the problem ?

What's more, the unit of R(r) should be 1 but now it is meter^-1.5

Thanks!

 

[alxm]

What's impossible about it? Looks fine to me.

 

[cgk]

The unit of the wave function is supposed to be length^(-3/2). If you square that you get a spatial probability density (unit: length^(-3)) and if you integrate that over the 3d space, you get a unitless quantity, cooresponding to a probability (1 in this case).

 

[caoyuan9642]

Oh that's true.
but how could I plot the whole wave function in 3D?
I just want to get the fantastic graph of the wave function.

 

[4tp]

one thing you may be forgetting is that the wavefunction itself is not immediately physical- ie any physical quantity will go like R^2 dV. try plotting R^2 r^2 to see the probability density of the electron.

 

[caoyuan9642]

It is quite good now.

The graph of 4$$\pi$$r² R₁₀(r)
comes to a peek when r/a=1

as can be seen.
thanks everybody.