
115Materials for Nanosensors
For L = 1 nm,
E
n h
m L q
1
e
eV= =
× ×
× × × ×
−
− −
2 2
2
2 34 2
31 9
8
1 6 626 10
8 9 1095 10 1 10
( ) ( . )
. ( )
22 19
1 60219 10
0 376
× ×
=
−
.
. eV
(2.46)
Similarly, E
2
, E
3
, E
4
, E
5
, … = 1.504, 3.384, 6.016, 9.4, … eV.
For L = 2 nm,
E
n h
m L q
1
e
eV= =
× ×
× × × ×
−
− −
2 2
2
2 34 2
31 9
8
1 6 626 10
8 9 1095 10 2 10
( ) ( . )
. ( )
22 19
1 60219 10
0 094
× ×
=
−
.
. eV
(2.47)
and E
2
, E
3
, E
4
, E
5
, … = 0.376, 0.846, 1.504, 2.35, … eV.
For L = 5 nm,
E
n h
m L q
1
e
eV= =
× ×
× × × ×
−
− −
2 2
2
2 34 2
31 9
8
1 6 626 10
8 9 1095 10 5 10
( ) ( . )
. ( )
22 19
1 60219 10
0 01504
× ×
=
−
.
. eV
(2.48)
and E
2
, E
3
, E
4
, E
5
, … = 0.06016, 0.13536, 0.24064, 0.376, … eV.
For L = 10 nm,
E
n h
m L q
1
e
eV=