Chemistry 302
Jan. 25, 2009
Quiz #1 Name
(Please Print)
Possibly Useful Constants & Info
h=6.626 ×10−34 Js c=2.998 ×108m/s NA= 6.02 x 1023
¯h= 1.054 ×10−34 Js me= 9.11 ×10−31kg
EP IB = n2h2/(8mL2)λ=h/mv
Please answer the following. You MUST show your work and give units.
1. (10 points) The Schr¨odinger equation is
b
Hψ(x) = E ψ(x). Define each term:
b
H, ψ(x),
and E.
Solution:
b
His the Hamiltonian operator for the object, given by −¯h2
2m
∂2
∂x2;
ψ(x) is the wave function of the object;
E is the energy of the particle;
(based on 1st week’s lectures; on Monday we learned about probability density)
2. (10 points) What is the deBroglie wavelength of an electron moving at a speed of 6.626×
105m/s? Pretend that these are Chem302 electrons, which have a mass of 1.0000. . . ×
10−30kg.
Solution: The expression for the deBroglie wavelength is λ=h/mv. Substitution
gives
λ=6.626 ×10−34J s
1×10−30 ·6.626 ×105·kg ·m/s =1×10−34
1×10−25 ·m= 1 ×10−9m = 1nm
1J= 1kg ·m2/s2; 1J s = 1kg ·m2/s
Score