Solution Set 2
1. MS 1-29: Using the deBroglie relation: = h / ( mv ) = h / (3mkT ) T =
h2 , hence 3mk2 T=2543 K. The higher the temperature, the higher the velocity, the smaller the wavelength. Small wavelengths are needed to achieve good resolution in n
Solution Set 3. Particle in the Box type problems.
1 MS-2.11. The wavefunction is oscillatory in both space and time. We can determine the
spatial period L (the wavelength) by examining the smallest non-zero L such that
y ( x + L, t ) = y ( x , t ) . Simi
Solution set 6, Chem 256
1. MS 6.10:
Using table 6.3 we find
2
2
3
3
3
3
3
3
sin 2 ei +
sin 2 e i +
cos 2 = 2 sin 2 +
cos2 =
8
8
4
8
4
4
The physical significance is that if we would have an electron in a p1 , p0 and a p1 orbital
the total electron densit
Solution set 7, Chem 256
1. MS 6.21
The probability to find the 1s electron within a sphere of radius R is given by ( a = a0 )
4
a3
z
z
a 4 2 2 r / a R 4 R 2 r / a
re
dr
+ 3 a re
0
0
2 a3
a 0
R
R2
4 a
a R 2 r / a
e
dr
= 2 2 e 2 R/ a 3 a re2 r / a 0 +
a
a
Solution Set 8, Chem 256
1. MS 8.5 1Eh =
e2 4 0a0
[ J ], h [ Js]. Hence the atomic unit of time is = h / Eh [s]. This
allows us to express c from m/s into a.u., using a0 / 2. MS 8.19
1 (1s (1)1s ( 2) 1s (1)1s ( 2) 2 1 (1s (1)1s ( 2 ) 1s (1)1s ( 2)* (1s (1