
501Nanobiosensors
f
k
m
0
14
5
1
2
1
2 3 14
0 07
7 826 10
1 506 10=
⎛
⎝
⎜
⎞
⎠
⎟
=
×
×
×
= ×
−
π
eff
Hz
.
.
.
.
(8.8)
When adsorbates are uniformly deposited on the cantilever surface, the
resultant mass change is
Δm
k
n
f f
= −
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
4
1 1
2
1
2
0
2
π
(8.9)
where f
1
and f
0
are the resonance frequencies after cantilever loading and
before loading. Equation 8.9 yields
100 10 10
0 07
4 3 14 0 24
1 1
1 506 10
12 3
2
1
2
5
2
× × =
×
( )
×
−
×
( )
⎛
⎝
⎜
⎜
⎜
⎞
⎠
− −
.
. .
.
f
⎟⎟
⎟
⎟
(8.10)
or,
1 10 7 395 10
1
4 4091 10
13 3
1
2
11
× = × × − ×
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
− − −
. .
f
(8.11)
or,
1 10
7 395 10
3 261 10
13
3
1
2
13
× =
×
− ×
−
−
−
.
.
f
(8.12)
or
f
1
= (7.395 × 10
−3
)/(4.261 × 10
−13
) = 1.73551 × 10
10
. Therefore f
1
= 1.31739 ×
10
5
Hz, and the freque ...