E 82√(+1) E (atomic unit) 2T V 2 ∫a"(a(uk=1∫+()(=1Ja+()p(nd=JB*(nkl(M=0 n( 2ax) xsin bxdx 4 sin( 2bx)---cos(2bx) d 2 h2k212 b x1(R)(R)=g6 ∑x(R)z2( Relative atomic mass: Ca-40 0-16 Work functions, o, are usually listed in units of electron volts, el wheree 1.602x10-J. What is the velocity of an electron emitted by Li(o=2.90ev )if light having a frequency of 4.77x10's" is absorbed? (4 points 2. Calculate the de broglie wavelength of an electron traveling at 1% of the speed of ight (0.01c=3.00x10%m/).(4 points) 3. Which of the following expressions are acceptable wavefunctions, and which are not? For those that are not, state why? (8 points 1)f(x)= 0<x<10 2)f(x)= 0<x<3 4 3)f(x) √x ,x≥0 4)f(x)=x2+1 4. Using Bohr interpretation, for an electron hav ing a one-dimensional wavefunction y=Nsin( a)in the range x=0 to 1, 1)Normalize the wavefunction 2) Calculate the probability that the electron is in the first half of the range, from x=0to0.5 3)Calculate the probability that the electron is in the middle half of the range, from x=0.25 to 0.75 4)Calculate the energy of this electron(assume that the potential energy is zero,  k v 2 1 = ( 1) 8 2 2 = J J + I h EJ  2 2 1 n E = − (atomic unit) *( ) ( ) = 1      d *( ) ( ) = 1      d *( ) ( ) = *( ) ( ) = 0       d     d ( ) sin( 2 ) 4 1 2 1 sin 2 ax a dx ax = x −  2 cos 2 2 2 c = a + b + ab cos(2 ) 8 1 sin( 2 ) 4 4 sin 3 2 2 bx b bx b x x x bxdx = − −  2 2 2 2 2 2 2 1 c l b k a h d = + + ij R  i (R) j (R) = g R (R) g a a R =   ( ) 1 * Relative atomic mass: Ca-40 O-16 1. Work functions,  , are usually listed in units of electron volts, eV , where 1 eV = J 19 1.602 10−  . What is the velocity of an electron emitted by Li (  = 2.90eV ) if light having a frequency of 15 1 4.77 10 −  s is absorbed? （4 points） 2. Calculate the de Broglie wavelength of an electron traveling at 1% of the speed of light ( 0.01c 3.00 10 m /s 6 =  ). (4 points) 3. Which of the following expressions are acceptable wavefunctions, and which are not? For those that are not, state why? （8 points） 1) x f x − = 4 1 ( ) , 0  x 10 ; 2) x f x − = 4 1 ( ) , 0  x  3 ; 3) f (x) =  x , x  0 ; 4) ( ) 1 2 f x = x + 4. Using Bohr interpretation, for an electron having a one-dimensional wavefunction  = N sin(x) in the range x = 0 to 1, 1) Normalize the wavefunction; 2) Calculate the probability that the electron is in the first half of the range, from x = 0 to 0.5 ; 3) Calculate the probability that the electron is in the middle half of the range, from x = 0.25 to 0.75. 4) Calculate the energy of this electron (assume that the potential energy is zero