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

caoyuan9642
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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!
 
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What's impossible about it? Looks fine to me.
 
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).
 
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.
 
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.
 
It is quite good now.

The graph of 4\pir2 R10(r)
comes to a peek when r/a=1
R1.JPG


as can be seen.
thanks everybody.
 
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