CHEM 442 Lecture 2 Problems
2-1. Which of the experimental results for the photoelectric effects suggest that light can
display particle-like behavior?
2-2. Why is a diffraction pattern generated by an electron beam formed by electrons
interfering with themselves rather than with one another?
2-3. Write down the formulas relating (a) frequency and wavelength, (b) wavelength and
momentum, and (c) energy and frequency of a photon.
2-4. Calculate the speed of a neutron with wavelength of 3.0 cm.
2-5. Calculate the de Broglie wavelength of an electron of an electron accelerated through
a potential difference of (a) 100 V and (b) 100 kV.
2-6. The work function for metallic rubidium is 2.09 eV. Calculate the kinetic energy and
the speed of electrons ejected by light with wavelength of (a) 650 nm and (b) 195 nm.
d
d
d
( cos x + i sin x ) , (b) sin 2 x , (c) ln x ,
dx
dx
dx
2
d ix
d -x
d 2
d
(d)
e , (e)
e , (f)
x cos x , (g)
cos y , where y = tan x .
dx
dx
dx
dx
2-7. Evaluate the following derivatives: (a)
2-8. Euler’s formula is eiq = cosq + isinq . Prove this by (a) showing that
d
ln ( cosq + i sinq ) = i , (b) integrating the both sides of the expression in (a) to obtain
dq
ln ( cosq + isinq ) = iq + C , (c) showing that C = 0, and (d) exponentiating the both sides
of the expression in (b) to obtain eiq = cosq + isinq .
2-9. Express the following complex numbers in the form reiq , where r and q are real
(corresponding to the absolute value and phase, respectively): (a) i , (b) -2 , (c) 1+ 3i ,
(
)
6
(d) 1+ 3i .
2-10. Evaluate (a)
i and (b) i i . Use 2-9 (a).