The wave function of 2s is given by 2 s = 1 2 2 ( 1 a 0 ) 1 / 2 ( 2 - r a 0 ) e - r / 2 a 0 At r = r 0 , radial node is formed. Thus, r 0 in terms of a 0 . [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
The wave function ( $Ψ$ ) of 2s is given by

$Ψ_{2 s} = \frac{1}{2 \sqrt{2 π}} {(\frac{1}{a_{0}})}^{1 / 2} (2 - \frac{r}{a_{0}}) e^{- r / 2 a_{0}}$

At $r = r_{0}$ , radial node is formed. Thus, $r_{0}$ in terms of $a_{0}$ . [2023]

1 $r_{0} = \frac{a_{0}}{2}$

2 $r_{0} = 2 a_{0}$

3 $r_{0} = 4 a_{0}$

4 $r_{0} = a_{0}$

Ans.
(2)

At node $Ψ_{2 s^{2}} = 0, Ψ_{2 s} = 0$

So, $(2 - \frac{r}{a_{0}}) = 0$

$2 - \frac{r_{0}}{a_{0}} = 0 \Rightarrow r_{0} = 2 a_{0}$

Want Us to Email you About Special Offers & Updates?