Applied Science and Innovative Research 

ISSN 2474-4972 (Print) ISSN 2474-4980 (Online) 

Vol. 7, No. 2, 2023 

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18 
 

Original Paper 

Discussion on the Problems of Bohr’s Hydrogen Atom Theory 

in Basic Theory 

Yuan Lixin1 

1 ShenZhen TELLUS holding co., ltd. Guang Dong China 

E-mail: wyyw112233@163.com 

 

Received: March 6, 2023       Accepted: March 13, 2023       Online Published: March 20, 2023 

doi:10.22158/asir.v7n2p18          URL: http://doi.org/10.22158/asir.v7n2p18 

 

Abstract 

According to the charge momentum and charge kinetic energy, it is proved that the key problem of the 

basic theory of Bohr hydrogen atom is that equation 
2

0

22

4 r

e

r

v
m











 does not hold. For the same 

electron of the hydrogen atom, the left side of the equation is the mechanical kinetic energy, the right 

side of the equation is the charge energy, the fundamental properties and the concept of energy are split. 

Based on experiments, this paper analyzes and calculates the combined energy of hydrogen, lithium and 

oxygen atoms, hydrogen atom radius mrH

10109772.1   and the ground state energy of 

hydrogen atom eVEH 6223.3  are obtained. This ground state energy HE  is basically 

consistent with the Balmer system of hydrogen atomic spectrum eV4.3 ; Electron around the nuclear 

velocity  smVe 6917.2 . hydrogen atom radius mrH

10109772.1  is calculated by using 

energy HE , which verifies the correctness of charge momentum and charge kinetic energy and their 

experimental basis. The ground state energy atom eV6.13  and radius mr 111029.5  of Bohr 

hydrogen is derived under the condition that the basic theory has problems and the theoretical formula 

is set to 1n , which has no experimental basis. The fundamental problem of quantum mechanics is that 

the theoretical formula of photoelectric effect is not correct, which is demonstrated in this paper. The 

relationship between the structure of hydrogen atom and the evolution of the universe is also discussed. 

Keywords 

problems, Bohr’s hydrogen atom theory, basic theory, charge momentum, charge kinetic energy, 

evolution of material structure, hydrogen atom radius, ground state energy, around the nuclear 



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velocity, quantum mechanics 

 

1. Preface 

Although great achievements have been made in the field of quantum mechanics, in fact, there are still 

serious problems in the basic theory. The “tunnel effect” is a typical non conservation theory of energy 

in quantum mechanics, and is the product of problems in the basic theory. The theoretical formula 

(Yang, 2014)   hmV 2

2

1
 of photoelectric effect is the basis of quantum mechanics “tunnel 

effect” and Bohr hydrogen atom theory. Because the formula of photoelectric effect theory is not 

correct, the “tunnel effect” and Bohr hydrogen atom theory have serious theoretical problems. 

Based on the charge momentum and charge kinetic energy (Yuan, 2015, 2016), this paper analyzes and 

studies the basic theoretical problems of Bohr hydrogen atom theory, “tunnel effect” and photoelectric 

effect theory. At the same time, the internal consistency and stages (Yuan, 2018) of the evolution of the 

energy structure of hydrogen atom and the evolution of the universe are discussed through the 

evolution of the material structure energy (Yuan, 2013, 2014). 

 

2. Charge Operation Mechanism Constructed by Charge Momentum and Charge Kinetic Energy 

Construction of Charge Momentum and Charge Kinetic Energy Mechanism (Yuan, 2015, 2016) 

Charge Momentum: QVP 
 

                                                      

(1)
 

Charge Kinetic Energy: 
2

2

1
QVW 

 
                                               

(2)

 

Where: Q is the charge and V is the charge velocity. 

According to equation (2), the equation of electron kinetic energy accelerated by electric field U can 

be established: 

21

2
eV eU

                              

(3) 

The electron velocity 2V U is obtained from equation (3). 

According to the momentum and kinetic energy properties of the charge, the centripetal force of the 

charge moving in a circle and the coulomb force equilibrium formula: 

2

2

0

2

4

1

r

e

r

V
e 


                              

(4) 

Get:
2

04

1

V

e
r 

  

Substituting 2V U  into the above formula, the solution is: 

U

e
re 

08

1


                             

 (5) 



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In formula (5), the atomic radius er  
is marked with angle mark e  because this radius is the result of 

deduction and calculation by electronic charges (3) and (4). In this paper, the related physical quantities 

determined by Bohr’s theory are marked with mass angle m , such as the radius mr of hydrogen atom, 

without further explanation. 

 

3. Basic Theoretical Problems in the Construction of Bohr’s Hydrogen Atom Theory 

3.1 Two Basic Formulas of Bohr’s Hydrogen Atom Theory 

Coulomb force of electrons running around the nucleus: 
2

0

22

4 mm r

e

r

V
m




 
                  

(6) 

Quantization of orbital conditions: mm nmVrL 
                                     

(7) 

The radius mr  of hydrogen atom is obtained from Formula (6) and (7): 









2

2

02

me

h
nr mm




 

  ,2,1n
                                                                     

(8) 

Let 1mn  in Formula (8), get: mrm

111029.5   

3.2 The Energy of Hydrogen Atom in Bohr Theory 

When the electron is running on a radius mr  orbit, the distance is selected as the zero point of the 

electrostatic potential energy of the system, and its electrostatic kinetic energy and potential energy are 

respectively (Jing, Du, & Jin, 2008): 

m

k
r

e
mVE

0

2
2

82

1


 ; 

m

p
r

e
E

0

2

4
  

Its total energy is: 

mmm

pkm
r

e

r

e

r

e
EEE

0

2

0

2

0

2

848 


                       

(9) 

Substituting the radius mr  of formula (8) into formula (9), the energy of hydrogen atom:  













22

0

4

2 8

1

h

me

n
E

m

m


                             

(10) 

Let 1mn  obtain from equation (10): 
22

0

4

8 h

me
Em




                                

(11) 

The solution is: eVEm 6.13

                                

 



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3.3 On the Basic Theoretical Problems of Bohr’s Hydrogen Atom Theory 

Bohr’s theory of hydrogen atom is based on the theory of photoelectric effect, and the problem lies in 

the basic theory of photoelectric effect. 

“According to Einstein, when light hits the metal surface, the photon with energy hv  is absorbed by 

the electron. The electron uses part of this energy to overcome its binding on the metal surface, and the 

other part is the kinetic energy of the electron after leaving the metal surface. This energy relationship 

can be written as: 

  hmV 2

2

1

                             

(12) 

That is, the energy hv  of the photon minus the binding energy (stripping work) of the electron in the 

metal is equal to the maximum kinetic energy of the electron.” 

As we know, electrons have mass and charge at the same time. The left side of formula (6) is the 

centripetal force of electron mass, and the right side is the coulomb force of electron. The left side of 

formula does not consider the movement of electron charge, but artificially establishes an equivalent 

physical relationship between the centripetal force of electron mass and the coulomb force of electron 

charge. 

The theoretical formula of photoelectric effect is based on the balance between photon mass kinetic 

energy 
2

2

1
mV  and electric field energy  h , while ignoring the main term of electric field 

energy balance of electron charge kinetic energy
 

2

2

1
QV . As a result, the ultra-high-speed running 

state of electron mass around the core is artificially caused, and the relativistic thinking of electron 

motion is introduced, which leads to the so-called “tunnel effect” and other basic theoretical problems 

in quantum mechanics. 

Considering the basic fact that electric charge flows to form current, how powerful electric energy will 

be generated when the outer electrons of hydrogen atom circle the nucleus at super high speed! 

Obviously, the ultrahigh speed movement of electrons around the nucleus is incorrect, and the 

theoretical formula of photoelectric effect is invalid. The energy non conservation of Bohr hydrogen 

atom theory and “tunnel effect” is the result of the problems in the basic theory of photoelectric effect. 

 

4. Calculate Hydrogen Atomic Radius with Chemical Reaction Energy of Hydrogen Oxide 

(Water) and Lithium Oxide  

“It has been proved from various experiments that the atomic radius is of the order of 
1010

. 

Therefore, the radius of the electron orbit will not be reduced to the size of the atomic nucleus, and the 

electron must run in a stable orbit with a radius of order of m1010
” (Zhu, 1979). The radius of the 



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Bohr hydrogen atom is mrm

111029.5  , which is much smaller than the average atomic radius, 

and it is very unusual. 

Therefore, it is necessary to confirm the radius of hydrogen atom on the basis of physical experiment. 

4.1 The Basis of Analogy between Hydrogen Atom and Lithium Atom 

Both hydrogen atom and lithium atom have a single electron in their outer shell, which is the closest in 

atomic structure and is highly comparable to each other in the periodic table. 

4.2 The Covalent Bonding Energy between the Elements is Determined by the Outer Electrons of 

Chemical Elements (Li & Feng, 1965). The Combination of Hydrogen and Lithium Atoms with Oxygen 

Atoms is Considered as the Combination Energy of the Outer Electrons of the Two Atoms with Oxygen 

Generation of hydrogen oxide (water): 

At C025  and 1 atmospheric pressure, 1 Grammolecule of hydrogen combines with 
2

1

 

Grammolecule of oxygen to form 1 Grammolecule of water:  

leGrammolecuKcalOHOH /4.68
2

1
222 

              

(13) 

Generation of lithium oxide (Ge, 1966): 

leGrammolecuKcalOLiOLi /143
2

1
2 22 

               

(14) 

Hydrogen atomic charge energy:

H

H
r

e
E

2

08

1



                                    

(15) 

Lithium atomic charge energy:

.

2

08

1

Li

Li
r

e
E 


                                      

(16) 

Let the outer electron charge energy of oxygen atom be: OE , Charge energy of the water molecules:

OHE
2

, Charge energy of lithium oxide molecules: OLiE
2

, Because the molecular charge energy is 

mainly determined by a single electron in the outer layer of hydrogen and lithium, so that

OLiOH EE
22

 , From the above: 

Combined energy of hydrogen and oxygen: JEEE OHOH

5106819.2
2



             

(17) 

Combined energy of lithium and oxygen: JEEE OLiOLi

5109858.5
2



              

(18) 

Formula (18) minus Formula (17): JEE HLi

5103039.3                            (19) 



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4.3 Hydrogen Atom Radius Determined by Combining Energy 

Substitute formula (15) and (16) into formula (19), and divide by the number of Grammolecule: 

23

52

0

2

0 1002.6

103039.3

8

1

8

1






J

r

e

r

e

HLi 
                      

(20) 

Substitute relevant physical constants and lithium atomic radius (Yang, Zhu, Zhao, & Lin, 1982)

pmrLi 152   

into formula (20), and get hydrogen atom radius: 

mrH

10109772.1 
             

              (21) 

Substitute hydrogen atom radius mrH

10109772.1 
 

into formula (15) to get Ground state 

energy of hydrogen atom: eVEH 6223.3  

The spectral energy level eV4.3 of Balmer spectrum in the contrast experiment is basically 

consistent. That is, the spectral energy level of Balmer spectrum is the ground state energy level of 

hydrogen atom. 

4.4 Testing Hydrogen Atom Radius er  in Formula (5) by Ground State Energy HE
 

of Hydrogen 

Atom 

Formula (5) is the result of the inference of charge momentum and charge kinetic energy. Through 

ground state energy HE of hydrogen atom, hydrogen atom radius er determined by Formula (5) is 

also a test of whether charge momentum and charge kinetic energy are correct or not. 

Substitute voltage VU 6223.3 of ground state energy into formula (5), 

 m
U

e
re

10
19

12

0

109772.1
6223.3

10602.1

109.88

1

8

1 












 

That is, He rr   

Therefore, charge momentum and charge kinetic energy have experimental basis and are correct. 

 

5. Analysis of the Operation of Hydrogen Atom by Kinetic Energy of Charge 

5.1 Hydrogen Atom Radius er and Hydrogen Atom Energy nE Determined by Kinetic Energy of Charge 

5.1.1 Analysis of the Movement of Hydrogen Atom Electrons around the Nucleus by Kinetic Energy of 

Charge 

Set to hydrogen atom radius er , and by formula (4), the electron runs around the core:  



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2

0

22

4 ee r

e

r

V
e




             

                   (22) 

Let the electron charge orbit condition be quantized: eee neVrL 
                     

(23) 

According to formulas (22) and (23), there are: 
3

2

02

e

h
nr ee






                            

(24) 

5.1.2 Hydrogen Atomic Energy eE   

When the electron runs on the orbit with radius er , the distance  is selected as the zero point of 

electrostatic potential energy, and its electrostatic kinetic energy and potential energy are respectively 

(Yuan, 2015; Jing, Du, & Jin, 2008):

 

e

k
r

e
eVE

0

2
2

82

1


 ,     

e

p
r

e
E

0

2

4


 

Total energy: 

eee

pke
r

e

r

e

r

e
EEE

0

2

0

2

0

2

848 


             

   (25) 

Substitute hydrogen atom radius of formula (24) into formula (25) to get eE : 













22

0

5

2 8

1

h

e

n
E

e

e


                             (26)
 

5.2 Discussion on the Value of 1 em nn   

The related data of Bohr’s hydrogen atom, such as ground state energy, radius and spectrum, are 

derived from Bohr’s hydrogen atom theory under the condition of 1mn . Therefore, the objective 

existence and rationality of the setting of Bohr’s hydrogen atom theory 1mn
 

should be analyzed 

and judged. 

5.2.1 Discussion on Hydrogen Atom Theory Corresponding to 1 em nn  

Let 1en , according to formula (26): eVEe

121039.2 
 

Compare eVEm 6.13-  with eVEe

121039.2  , The system energy of the same substance 



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should be the same, but under the condition of 1 em nn , there is a huge energy difference 

between hydrogen atoms electron mass kinetic energy and electron charge kinetic energy in the same 

system, which is obviously illogical. 

Let 1en , according to formula (24), hydrogen atom radius: 

mre

22100248.3   

Divide equation (8) by equation (25): 
m

e

n

n

r

r

e

m

e

m 
2

2

  

                                   (27) 

5.2.2 Analysis of Equation (27) 

(1) The correlation between radius mr  
and er  

determined by equation (27) 

Let em rr  , 1mn , then formula (27): 1
1

2


m

e

ne

, solve:  

m

e
ne 

                              

(28) 

(2) Substituting hydrogen’s ground state energy eVEH 6223.3  into the formula (26), solve: 

5

0

2

100861.8
226223.3

1


h

e
ne


         

          (29) 

Substituting 
5100861.8 en into (26) is as follows: 

  













22

0

5

25 810.08618

1

h

e
Ee


                

      (30) 

According to the general expansion of hydrogen atom spectrum by formula (30), the spectral frequency 

corresponding to the energy level is: 

When 1k , it is the Balmer system spectrum 

 
 
























2232

0

5

25

11

810.08618

11~

nkch

e
EE

ch
kn


  ( ,4,3,2n )   (31) 

5.2.3 Discussion on the Physical Meaning of When 1n  

From the quantization of the electron mass orbital condition a, when 1n  is the starting point of the 

quantization condition. The implicit premise of setting 1n  is to treat the hydrogen atom as an 

immutable structure, that is, the present hydrogen atom structure is still at its original starting 

point.Does the structure of the hydrogen atom not evolve for billions of years? This is obviously 



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inconsistent with the fact that the structure of matter can evolve (Yuan, 2013), the decay (Yuan, 2009) 

of nuclides and the decay (Guo, Zhao, & Peng, 2010) of element  . 

Thinking about 1
0

 em nn
 

is equivalent to thinking about the current state of the hydrogen atom 

as the beginning of the evolution of the universe, the beginning of the process. How is it possible to 

determine the ground state energy of a hydrogen atom exactly in terms of 1
0

 em nn ? It is 

precisely because the ground state energy eV6.13 of the hydrogen atom given by 1mn  is 

that it will be abnormally different from its similar alkali metal work out (Wang & Zhou, 2008): 

lithium (Li) 2.49 eV , natrium (Na) 2.28 eV , and kalium (K) 2.22 eV . 

The evolution of the universe is a process, so is the evolution of the material structure (Yuan, 2018). 

How can we think that today, billions of years after the evolution of the universe, the structure of the 

hydrogen atom can be set to 1mn
 

for calculation? Therefore, the actual physical meaning implied 

by the initial state value is worthy of careful study. 

Physics is based on experiments and exists in reality. The historical process of material evolution has 

been merged into the constants of physical formulas through physical experiments. In other words, the 

essential meaning of physical constants is the historical precipitation in the process of material 

evolution, which is the bridge between the present and history. The evolution of the universe and the 

change of the structure and energy of matter determine that it is impossible for Bohr’s theory of 

hydrogen atom to coincide with the actual state of the current evolution of the universe under the 

condition of 1n . 

5.3 The Discussion about Electron Mass Kinetic Energy and Electron Charge Kinetic Energy 

When electron e  moves in electric field (Yuan, 2015) 12 EEU  , the kinetic energy of electron 

motion should be the sum of electron mass kinetic energy and electron charge kinetic energy. 

Formula (3) shall be expressed as: 

  eUVem  2

2

1
                            (32) 

Then the total energy of the electron is: 

 
r

e
Vem

0

2
2

82

1




                         

(33) 

Because 
22

2

1

2

1
mVeV  , ignore 

2

2

1
mV , equation c can be rewritten as:

 

r

e
eV

0

2
2

82

1




                 

          (34)

 



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By formula (32) and (34), there are:
r

e
U

08


        

                                (35) 

5.4 A Discussion of the Electron Velocity of Hydrogen Atom around the Nucleus as Determined by 

Equations (4) and (6) 

Hydrogen atom radius is mre

10109772.1   in Equation (4), and hydrogen atom radius is radius 

mrm

111029.5  in Equation (6),  

From Equation (4), we can get: 

 sm
r

e
V

e

e 6917.2
109772.1109.84

106021.1

4 1012

19

0











   
     (36) 

From Equation (6), we can get: 

)/(101846.2
1029.5109.8101.94

106021.1

4

6

111231

19

00

sm
rm

e
V

m

m 










 (37) 

Compared with the calculation results of formula (36) and formula (37), the velocity deviation between 

 smVe 6917.2 and )/(101846.2 6 smVm   is huge, and the electron velocity mV
 

calculated by formula (6) can’t explain the Huge electric field energy problem caused by electron 

charge in such high-speed motion. 

It can be seen that the thinking of Formula (6) is unreasonable. According to Equation (4), the motion 

velocity smVe 6917.2
 

of the electron around the nucleus can be obtained. It can be seen that the 

motion of the electron around the nucleus is very low, so there is no need to consider relativity. 

 

6. Conclusion and Discussion 

This paper demonstrates the problems existing in the basic theory of Bohr’s theory of hydrogen atom 

through two ways. 

First, it demonstrates the ground state energy eE of the hydrogen atom, hydrogen atom radius er , the 

motion velocity eV
 
of the electron around the nucleus, and hydrogen atom spectrum with the theory 

construction of charge momentum and charge kinetic energy, and demonstrates the irrationality of these 

four physical quantities of Bohr’s theory of hydrogen atom theory. And from the aspect of evolution of 

the universe, the irrationality of the condition setting of Bohr’s theory of hydrogen atom theory n 

equals 1 is demonstrated. 



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Second, the experiment of hydrogen atom structure is demonstrated by the combined reaction energy of 

hydrogen oxide (water) and lithium oxide. the ground state energy eE of the hydrogen atom and 

hydrogen atom radius er were calculated, and the experimental basis of hydrogen atom theory was 

constructed. 

It is proved that hydrogen atom radius er  
and Hr  

obtained by the two approaches are equal, which 

also proves the correctness of the construction of charge momentum and charge kinetic energy theory 

and its experimental basis. According to ground state energy HE of the hydrogen atom obtained in this 

paper, when hydrogen atom obtains the ground state excited energy eV6223.3 , it will radiate 

Balmer spectrum, and it is impossible to appear the excited radiation state of the energy eV6.13 . 

In theory construction, a theory construction chain phenomenon is often formed. If there are problems 

in the basic theory of this construction chain, it may become an insurmountable obstacle of theoretical 

research chain, which not only produces some wrong understanding, but also leads the artificial 

interpretation of relevant 

experimental data. In the aspect of physics research and the solution of related problems, we will find 

that people tend to use equivalence, fitting and empirical formula consciously or unconsciously to 

bypass the problems existing in the basic theory and solve the problems encountered in an empirical 

way. For example, “tunneling” is used to explain nonconservation of energy (Yuan, 2018) that cannot 

be explained by quantum mechanics. In astrophysics, empirical formulas are fitted with experimental 

data to solve the problems of satellite orbit (Yuan, 2012). Such thinking and analysis methods not only 

affect our theoretical thinking, but also affect our correct analysis of experimental results. 

We should pay careful attention to the thinking of problems in basic theory, which is the root of 

theoretical construction. We should not be too confident in the construction of basic theory. We should 

re-examine and rethink the basic theory, including the construction of the basic theory of astrophysics 

(Yuan, 2022). 

 

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