corrigé - Physique

TD3 : Physique quantique – corrigé
Exercice 1   
  E1       −,               
          E2→E1         E=
−13 .6×(1/4 −1) = ,           λ=  
     E1                
          n   n0n > n0  
E=En−E0
n=E11
n2−1 n02=hc λ
1
λ=−E1 hc 1 n02−1 n2 R=−E1 hc ',×−
      E2      λ1=R1
22−1 32−1= 654   λ2=
R1
22−0−1= 364              
 E3 λ2=R1
32−0−1= 818             
séries
λ
I
                  cf      
         E1          
Exercice 2   
     E=hc
λ=, ×− =, 
  n           P   P=nE  n=P/E=
×−/, ×− =, × −
  N=nt      t         l=ct    
V=πr2l=πr2ct       d=N
V=n πr2c=, × −=, ×−
Exercice 3   
 E=hc/λ=, ×− 
         r=d(α/2)    S=πr2=πd22(α/2)   I
        I=P/S=P/(πd22(α/2)) = ,  −
    γ=P/P =P/(U I)'47
            ne=I/qe=−/,×− =, ×−
         np=P/E=, × −        
γq=np/ne'47                  
Exercice 4   
             ,       
 λ=hc/E=,     
           λ2= 550   E2=hc/λ2    
      E=,     r     
   γ=rE/E2=r(hc/λ)/(hc/λ2) = r(λ2/λ) = 0 .49 ×r < r
Exercice 5         
     E=hf         n=P/E=P/(hf ) = , × −
                granulaire   
Exercice 6   
                  µ
           λ=h/p=h/(mv)  v=h/(mλ)  λ=   
v=, × −    E= 1/2mv2=, ×− =, ×−   
      , 
       E=, ×−
  E=    λ=, ×−           

Exercice 7    
    λe   r   λe=h
mv =s4πε0h2r mq2
        L= 2πrn=nλe=ns4πε0h2rn
mq2       
4π2r2
n=n24πε0h2rn
mq2 rn=ε0h2 πmq2n2
 En=−q2
8πε0rn
=−mq4
8ε2
0h2n2=−E1
n2 E1=mq4 8ε2
0h2
       En En0       E=En−En0=hc/lambda   
1
λ=En−En0 hc =E1 hc 1 n02−1 n2=R1 n02−1 n2 R=mq4 8ε2
0h3c
   R=, ×− E1=−, 
     F=1
4πε0
q2
r2       noyau-électron Fr=mar=mv2/r
         r     E      
Ec= 1/2mv2     Ep=−1
4πε0
q2
r
Exercice 8    
 •   E0=, ×− =,×− λ0=h/mv  E= 1/2mv2 v=p2E/m
λ0=h/√2mE =, ×− 
•   Ec=, ×− =,×−  λc=,×− 
•   Ef=,×− =,×−  λf=,×− 