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

Answer: (C)

$4\,\pi \,{{r}^{2}}\,dr\,{{\psi }^{2}}$

Answer 2

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 $\sigma =4\pi {{r}^{2}}dr{{\psi }^{2}}$