For an in a H-atom, is proportional to . What is the ratio of the probability of finding the at the nucleus to the probability of finding it at (Bohr's radius)?

Question

For an  in a H-atom,  is proportional to . What is the ratio of the probability of finding the  at the nucleus to the probability of finding it at  (Bohr's radius)?

Canvas Classes · Accepted Answer

Step 1: Probability density

Probability density

Step 2: At the nucleus (r = 0)

However, the probability of finding the electron at the nucleus (a single point) involves the probability density multiplied by the volume element .

At : the volume element

So the probability (not probability density) at the nucleus =

Step 3: Conclusion

The probability of finding the electron exactly at the nucleus (a mathematical point) is zero, because the volume element  at .

Final Answer: Zero → Optio

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