Question

Chemistry

Posted 3 months ago

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6. Calculate the most probable radius at which an electron will be found when it occupies a 1s orbital of a hydrogen atom.
$\text { hint: } \begin{aligned}
& \Psi_{1 s}(x)=\frac{1}{\sqrt{\pi}}\left(\frac{1}{a_{0}}\right)^{\frac{3}{2}} e^{-\frac{x}{a_{0}}} \text {; } a_{\circ} \text { is the Bohr radius } \\
& \text { radial probabilit } p(r)=4 \pi r^{2}\left|\Psi_{1 s}(x)\right|^{2}
\end{aligned}$
```

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Answer from Sia

Posted 3 months ago

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Answer

The most probable radius at which an electron will be found when it occupies a 1s orbital of a hydrogen atom is the Bohr radius $a_0$.

Key Concept

The most probable radius for an electron in a 1s orbital is found by maximizing the radial probability density function.

Explanation

The most probable radius is the value of $r$ at which the radial probability density function $p(r)$ reaches its maximum. For a 1s orbital, this occurs at the Bohr radius $a_0$.

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