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1
IAT (IISER) 2022
MCQ (Single Correct Answer)
+4
-1

Which of the following expressions represents the hydrogen atom wave function $\psi(r)$ shown in the figure below? ( $r$ is the distance of the electron from the nucleus and $a_0$ is a constant)

IAT (IISER) 2022 Chemistry - Atomic Structure Question 1 English
A
$\cdot \frac{1}{\sqrt{\pi}}\left(\frac{1}{a_0}\right)^{3 / 2} e^{-r / 2 a_0}$
B
$\frac{1}{\sqrt{6 \pi}}\left(\frac{1}{a_0}\right)^{3 / 2}\left(\frac{r}{a_0}\right) e^{-r / 2 a_0}$
C
$\frac{1}{4 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{3 / 2}\left(2-\frac{r}{a_0}\right) e^{-r / 2 a_0}$
D
$\frac{1}{\sqrt{3 \pi}}\left(\frac{1}{a_0}\right)^{3 / 2}\left(3-\frac{2 r}{a_0}+\frac{2 r^2}{9 a_0^2}\right) e^{-r / 3 a_0}$
2
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1
The total number of nodes for a given principal quantum number $n$, and azimuthal quantum number $\ell$, are
A
sum of $\ell$ angular nodes and $n+\ell-1$ radial nodes
B
sum of $\ell$ angular nodes and $n-\ell-1$ radial nodes
C
sum of $\ell+1$ angular nodes and $n-\ell-1$ radial nodes
D
sum of $\ell+1$ angular nodes and $n+\ell-1$ radial nodes
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