Question

For hydrogen atoms, the 2pz state (n = 2, l = 1, m = 0) is described by wavefunction

$\Psi _{_{_{210}}} = \frac{1}{\sqrt{32\pi }}\left ( \frac{1}{a_{0}} \right )\sigma e^{-\sigma/2 }cos\Theta$   $\left ( \sigma =\frac{r}{a_{0}} \right )$

a. What are the values of the total angular momentum L and its z-component Lz?

b. Show that this wavefunction is normalized.

You may need the following integral:

$\int_{0}^{\infty }x^{n}e^{-x}dx=n!$

Answer 1

a. L= Jereti ħ {= Ji(+1) h 1 Po z = mh for, 4210 > 2=1 h her hore m=0 So, Total angular momentum, i= 2t and it's e Component, Lzz mn=o.

*240 = f (tore=ph.coso (ru a) 32 T - Nis normalization Conostant To show Normalized we have to show, <4210 1*20) =1. no. 2r (come Sao) - eft nu jao o iter are se le porn site me pro tone cas järgat per (to)? S dr. the *. (3)(w) -1. 321 32T

Jae-sine.com - zidu. - [31 --, ti Cose -re, drz-Sina.do. &. 94. erao. dr = 3 aš xhe?de = a8.4! = 2495 let a = x =) draaoa

=> 1 2 (t.)".(05).240.620) » 1= .aona / So, n? 20 | N=1 km The wave function is not normalized. So, the normalized wave function would will be. those who loo (10.) 6-ho.cose.