Question

The radial part of the Schrodinger wave equation for hydrogen atom is given below :

$\gamma \left(r\right)=\frac{1}{16\sqrt{4}{a}_0^{3/2}}(\sigma -1)({\sigma }^2-8\sigma +12){\theta }^{-\sigma /2}$

Here, $a_0=$ constant, $\sigma =\frac{2r}{n{a}_0}$ and $n=$ principal quantum number.

With respect to the above-given data, select the correct statements.

• A. Distance of the nearest radial node from the nucleus is $2a_0$.
• B. Distance of the farthest radial node from the nucleus is $12a_0$.
• C. Number of maxima in the curve $\gamma \left(r\right)$ vs $r$ is $4$.
• D. The given equation of $\gamma \left(r\right)$ represents $4p$ orbital.

Answer 1

Answer: (A), (B), (C)

The correct options are
A Distance of the nearest radial node from the nucleus is $2a_0$.
B Distance of the farthest radial node from the nucleus is $12a_0$.
C Number of maxima in the curve $\gamma \left(r\right)$ vs $r$ is $4$.

The radial nodes occur when the radial probability function equals zero.

$(\sigma -1)({\sigma }^2-8\sigma +12)=0$

$\sigma =1,2,6$

$\frac{2r}{n{a}_0}=1$ is the nearest radial node.

For n=4,

$r=2a_0$

$\frac{2r}{n{a}_0}=6$ is the farthest radial node.

For n=4,

$r=12a_0$