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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
No.3
Solution
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
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
 = =
=
=
= =
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Allowed Energy Levels.pdf

  • 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
  • 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 = = = = = =