One of the maximum value of R2 lies approximately atThe r-dependent wave function of hydrogen atom is given by the expressionR=( constant )2ra0−r23a02exp⁡r/3a0Answers the following questions.

# One of the maximum value of ${\mathrm{R}}^{2}$ lies approximately atThe r-dependent wave function of hydrogen atom is given by the expressionAnswers the following questions.

1. A

$r=2.0{a}_{0}$

2. B

$r=4.0{a}_{0}$

3. C

$r=11.47{a}_{0}$

4. D

$r=12.5{a}_{0}$

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### Solution:

For the maximum or minimum, the first derivative of R with respect tor will be equal to zero

Hence $-\frac{2}{{a}_{0}}+\frac{4r}{9{a}_{0}^{2}}-\frac{1}{{a}_{0}}+\frac{2r}{3{a}_{0}^{2}}-\frac{2{r}^{2}}{27{a}_{0}^{3}}=0$

or $\frac{2{r}^{2}}{27{a}_{0}^{2}}-\frac{10r}{9{a}_{0}}+3=0$ or $2{\left(\frac{r}{{a}_{0}}\right)}^{2}-30\left(\frac{r}{{a}_{0}}\right)+81=0$

Solving for $r/{a}_{0}$, we get