YouTube Lecture # 1

1. 1
An electron is
trapped in a one-
dimensional region of
width 0.050 nm. Find
the three smallest
possible values
allowed for the
energy of the
electron.
Helping Tools
No.1
No.2

2. 2
No.3
Solution

3. 3
2 2
2
2 2 2
1 2 2 2
2
2 2
2
6 2
2 2
2
We know that smallest
energy requires 1 in
equation
8
8 8
( )
8( )
(1240 . )
8 (0.511X10 eV) X(0.050 nm)
1537600( ) (nm)
150.45
10220 ( )
n
n
n h
E
mL
h h c
E X
mL mL c
hc
mc L
eV nm
X
eV
eV
eV nm
=
=
 = =
=
=
= =
2 2 2
2 2 2 2
2
2 2
2
6 2
2 2
2
4
8 2
( )
2( )
(1240 . )
2 (0.511X10 eV) X(0.050 nm)
1537600( ) (nm)
601.8
2555 ( )
h h c
E X
mL mL c
hc
mc L
eV nm
X
eV
eV
eV nm
 = =
=
=
= =

4. 4
2 2 2
3 2 2 2
2
2 2
2
6 2
2 2
2
9 9
8 8
9( )
8( )
9(1240 . )
8 (0.511X10 eV)X(0.050nm)
13838400( ) (nm)
1354.05
10220 ( )
h h c
E X
mL mL c
hc
mc L
eV nm
X
eV
eV
eV nm
 = =
=
=
= =