The electron can make transitions from the n=5 state to the n=3, n=2, n=1, and n=0 states in hydrogen. The energies of the radiations emitted from these transitions are 0.306 eV, 0.966 eV, 2.856 eV, and 3.56 eV, respectively. These values are calculated from the energy levels of the Bohr model for hydrogen.

1. 1
An electron is in
the n = 5 state of
hydrogen. To
what states can
the electron
make transitions,
and what are the
energies of the
emitted
radiations?

2. 2
Helping Tools
No.1
OR
OR
OR

3. 3
Solution
2
1
2
3
4
5
We know that energies of Bohr
orbits in hydrogen are given by:
13.60
( 1,2,3,...)
13.60
13.60
3.4
4
13.60
1.51
9
13.60
0.85
16
13.60
0.544
25
n
eV
E n
n
E eV
eV
E eV
eV
E eV
eV
E eV
eV
E eV
−
= =
 = −
−
 = = −
−
 = = −
−
 = = −
−
 = = −
5 4
5 4
0.544 0.85
0.306
,
Transition from n to n
E E E
eV eV
eV
Now
= =
 = −
= − +
=

4. 4
5 3
5 3
0.544 1.51
0.966
,
Transition from n to n
E E E
eV eV
eV
Now
= =
 = −
= − +
=
5 2
5 2
0.544 3.4
2.856
,
Transition from n to n
E E
N
E
eV
w
V
eV
o
e
= =
 = −
= − +
=
5 1
5 1
0.544 13.6
3. 56
,
1 0
Transition from n to n
E E E
No
eV eV
eV
w
= =
 = −
= − +
=