Question

Which one of the following expressions represent the electron probability function ?

• A. $ 4\,\pi \,r\,dr\,{{\psi }^{2}} $
• B. $ 4\,\pi \,{{r}^{2}}\,dr\,\psi $
• C. $ 4\,\pi \,{{r}^{2}}\,dr\,{{\psi }^{2}} $
• D. $ 4\,\pi \,r\,dr\,\psi $

Answer 1

The Correct Option is C

The radial probability distribution of electron may be obtained by plotting the function $ \text{4}{{\text{ }\!\!\pi\!\!\text{ }}^{\text{2}}}{{\text{r}}^{\text{2}}}\text{R}_{\text{n,l}}^{\text{2}} $ against r, its distance from the nucleus. Such graphs are known as radial probability distribution curves. Similar curves are obtained if the complete wave function $ \psi $ is taken in the expression $ 4{{\pi }^{2}}{{R}^{2}}.dr. $ when the latter becomes $ 4{{\pi }^{2}}{{r}^{2}}{{\psi }^{2}}dr. $ So, the probability function $ \sigma =4\pi {{r}^{2}}dr{{\psi }^{2}} $