Question

What is the difference between the probability density and the radial probability density?

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a.)\textbf{a.)} We have to find angular momentum of hydrogen atom in a 6s6s state.

We know that, the 6s6s state is described by n=6n=6 and l=0l=0 .

So, from equation for the orbital angular momentum, we have :

L=l(l+1)L=0(0+1)L=0\begin{align*} L&=\sqrt{l(l+1)}\hbar\\ L&=\sqrt{0(0+1)}\hbar \tag{Substitute values in equation.}\\ L&=0\\ \end{align*}

b.)\textbf{b.)} We have to find angular momentum of hydrogen atom in a 4f4f state.

We know that, the 6s6s state is described by n=4n=4 and l=3l=3 .

So, from equation for the orbital angular momentum, we have :

L=l(l+1)L=3(3+1)L=3(4)L=12\begin{align*} L&=\sqrt{l(l+1)}\hbar\\ L&=\sqrt{3(3+1)}\hbar \tag{Substitute values in equation.}\\ L&=\sqrt{3(4)} \hbar\\ L&=\sqrt{12}\hbar\\ \end{align*}

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