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Question

The wavefunction of a 2s electron is given by ψ2s=142π(1a0)32(2ra0)era0
It has a node at r=r0. The value of r0a0 is___


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Solution

ψ2=132π2(1a0)3(2ra0)2e2ra0
When r=r0, it has a node (i.e.) ψ2=0
132π2(1a0)3(2r0a0)2e2r0a0=0
From this relation it is clear that any of these terms
(i.e)132π2(or)(1a0)3(or)(2r0a0)2(or)(e2r0a0) has to be equal to zero.
It is only possible for (2r0a0) to be equal to 0, all the others cannot ever become zero

Hence, 2r0a0=0(or)r0a0=2


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