1
ENSC 3313, Spring 2005
TEST 1  KEY
Name_________________________
Answer all 10 questions, show all work, 2points each
1.
Each color pixel in a video image of a standard television is renewed 30 times/s. The pixel light intensity
decays exponentially with time after being renewed.
Calculate the decay constant for the phosphor pixel if 80%
or less of the intensity is to remain at the next renewal.
Answer:
Exponential decay problem
τ
−
=
t
0
e
I
I
τ
−
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
t
I
I
ln
0
solve for
τ
:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
τ
0
I
I
ln
t
We need the intensity to decay to
≤
80%, so I/I
0
=0.80 and this must occur by t =1/30 s.
Plug in numbers:
s
15
.
0
)
80
.
0
ln(
30
/
1
=
−
=
τ
2.
A silicon single crystal is grown such that, when sliced into wafers, the (001) plane of atoms is exposed.
Calculate the number of silicon atoms per cm
2
on the (001) plane.
Note: Si has diamond cubic crystal structure
(illustrated) of side length a=0.543 nm, atomic radius = 0.118 nm, and N
A
= 6.023
×
10
23
mol
1
.
Answer:
The (001) plane is the top face of the unit cell.
There are two atoms per unit area on this plane,
hence the planar density of atoms is:
2
14
2
7
cm
atoms
Si
10
8
.
6
nm
cm
10
nm
543
.
0
2
.
D
.
P
×
=
⎟
⎠
⎞
⎜
⎝
⎛
×
=
−
x
y
z
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 Fall '11
 staff
 atoms, Crystal, Diamond cubic, Atomic packing factor

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