edit
The energy of the hydrogen atom is calculated using the following equation:
'''Energy of Hydrogen Atom'''
E
=
−
(
m
e
e
4
32
π
2
ϵ
0
2
h
2
)
1
n
2
{\displaystyle E=-\left({\frac {m_{e}e^{4}}{32\pi ^{2}\epsilon _{0}^{2}h^{2}}}\right){\frac {1}{n^{2}}}}
To calculate the change in energy required to go from the ground state to n=2, the following equation is used:
δ
E
=
−
(
m
e
e
4
32
π
2
ϵ
0
2
h
2
)
1
n
2
+
(
m
e
e
4
32
π
2
ϵ
0
2
h
2
)
1
n
2
{\displaystyle \delta E=-\left({\frac {m_{e}e^{4}}{32\pi ^{2}\epsilon _{0}^{2}h^{2}}}\right){\frac {1}{n^{2}}}+\left({\frac {m_{e}e^{4}}{32\pi ^{2}\epsilon _{0}^{2}h^{2}}}\right){\frac {1}{n^{2}}}}
δ
E
=
−
(
m
e
e
4
32
π
2
ϵ
0
2
h
2
)
1
4
+
(
m
e
e
4
32
π
2
ϵ
0
2
h
2
)
1
1
{\displaystyle \delta E=-\left({\frac {m_{e}e^{4}}{32\pi ^{2}\epsilon _{0}^{2}h^{2}}}\right){\frac {1}{4}}+\left({\frac {m_{e}e^{4}}{32\pi ^{2}\epsilon _{0}^{2}h^{2}}}\right){\frac {1}{1}}}
δ
E
=
(
m
e
e
4
32
π
2
ϵ
0
2
h
2
)
5
4
{\displaystyle \delta E=\left({\frac {m_{e}e^{4}}{32\pi ^{2}\epsilon _{0}^{2}h^{2}}}\right){\frac {5}{4}}}
δ
E
=
(
(
9.10938
x
10
)
−
31
k
g
(
1.60218
x
10
−
19
c
)
4
32
π
2
8.854
x
10
1
2
c
2
S
2
/
k
g
m
2
)
2
(
1.054
x
10
−
24
J
.
s
)
2
)
5
4
{\displaystyle \delta E=\left({\frac {(9.10938x10)^{-31}kg(1.60218x10^{-19}c)^{4}}{32\pi ^{2}8.854x10^{1}2c^{2}S^{2}/kgm^{2})^{2}(1.054x10^{-24}J.s)^{2}}}\right){\frac {5}{4}}}
δ
E
=
(
(
9.10938
x
10
)
−
31
k
g
(
1.60218
x
10
−
19
c
)
4
32
π
2
8.854
x
10
1
2
c
2
S
2
/
k
g
m
2
)
2
(
1.054
x
10
−
24
J
.
s
)
2
)
5
4
{\displaystyle \delta E=\left({\frac {(9.10938x10)^{-31}kg(1.60218x10^{-19}c)^{4}}{32\pi ^{2}8.854x10^{1}2c^{2}S^{2}/kgm^{2})^{2}(1.054x10^{-24}J.s)^{2}}}\right){\frac {5}{4}}}
δE =((9.10938x10)−31kg(1.60218x10−19c)432π28.854x1012c2S2/kgm2)2(1.054x10−24J.s)2)54
