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Chapter 41: Q. 10 (page 1206)

The hydrogen atom1swave function is a maximum atr=0. But the1s radial probability density, shown peaks at r=aB and is zero atr=0. Explain this paradox.

Short Answer

Expert verified

The given statement is proved.

Step by step solution

01

Given Information

We need to prove peaks at r=aBand is zero atr=0.

02

Explanation

The radial probability density Prr=4蟺r2Rnlris the probability density for finding the electron at a distance from the nucleus. The radial wave function Rlsris a maximum at the origin. the origin is the point for finding the electron. The probability density Pris smaller at any one point r=aBthan the origin. Since there are many points having r=aBonly a single point r=0mThe increased number of points more than compensates for the decreased probability per point. As a result, finding the electron at a distance r=aBSo, it is at a distance r=0m.

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