Optics and Photonics Journal, 2011, 1, 36-42
doi:10.4236/opj.2011.12006 Published Online June 2011 (http://www.SciRP.org/journal/opj/)
How Fast a Hydrogen Atom can Move Before Its Proton
and Electron Fly Apart?
Wei-Xing Xu
Newtech Monitoring Inc., Oshawa, Canada
Received March 17, 201 1; revised April 15, 2011; accepted April 25 , 2011
Abstract
In this paper we discussed the behavior of a hydrogen atom in moving and found there is a speed threshold
for hydrogen atom. As long as the speed of hydrogen reaches or beyond its speed threshold, the proton and
electron in hydrogen atom will fly apart. We also discussed the effect of the movement of hydrogen atom on
its absorption spectrum which is important in spectrum analysis.
Keywords: Redshift, Blue Shift, Speed Threshold, Hydrogen Ionized, Time Travel
1. Introduction
Einstein’s theories of special and general relativities chang e
our opinion about the universe [1,2]. The new concepts
such as time inflation and curved spacetime frequently
appeared in scientific pub lications. Some idea developed
from Einstein’s theory even causes the imagination of
the fiction novel writer and they write a lot of books re-
garding the time travel [3,4]. Meantime, some scientists
mainly focus on how to make the time travel theoreti-
cally possible. The reason why human beings are so in-
terested in time travel is in that based on the Einstein’s
theory, the people can live much longer by time travel.
This dream for long life ignites the human beings’
speculation on the universe we lived in.
Until now so many proposals about time travel have
been published in scientific jour nals. Kurt Goedel pointed
out the closed time like curves (CTCs) may make the
time travel possible [5]. Deutsch also proposed a Hilbert-
space based theory [6]. H. G. Well even designed the
time machine which can be used for time travel, just like
space shuttle [7]. Morris et al. try to develop the quan-
tum mechanics based the closed time like curve, there-
fore, the concept of worm hole is proposed [8]. Even
more recently, the quantum mechanics of time travel is
still actively discussed in literatures [9-12].
In this paper, we will not focus on the difference among
the theories regarding the time travel. Instead, we will
study the behavior of a hydrogen atom in moving and its
effect on the excitation spectrum of hydrogen atom,
which may give us some clue about the time travel.
2. Speed Threshold for Hydrogen Atom
For a system including a free electron and proton, total
energy of the system is:
'0 02
()
ne
mmc   (1)
Where 0
n
mand 0
e
mare the masses of proton and elec-
tron at rest respectively. c is the speed of light in vacuum.
'

is the Lawrence factor.
When the proton and electron combined together to
form a hydrogen atom, total energy of system becomes
4
00 2
2222
0
8
ne e
mm c
nhc






, where 00
00
ne
ne
mm
mm
  (2)
If we accelerate the hydrogen atom, total energy of
system increases. When total energy of system reaches or
more th an'0 02
()
ne
mmc  , then the proton and electron in
hydrogen atom will fly apart, that is,
4
00 2'002
ne
2222
0
(mm )c
8
ne e
mm c
nhc




 

 (3)
00
'4
00 2222
0
8
ne
ne
mm
e
mm nhc






(4)
'2
00
2
4
200 2222
20
1
18
ne
ne
vmm
ce
vmm nhc
c










(5)

W. X. XU
37
2
'2
00
2
24
00
2 2222
0
1
18
ne
ne
vmm
c
ve
mm
cnhc



 





(6)
2
'2 4
00
2 2222
20
2002
18
1()
ne
ne
ve
mm
cnhc
v
cmm


 

 
 
  (7)
2
2'2 4
22222200
0
1(1)18()
ne
vv e
ccnhcmm



 



(8)
'2
222
2
1(1)(1)
v
vc
c


 


,
where 4
222200
0
8()
ne
e
nhc mm

  (9)
'2'2 '2
22 22
222
22
vvv
vc
c cc
 

 


(10)
12
'2'2 '2
22
222
22
vvv
vc
c cc
 

 


(11)
For n = 1 and '
v = 0, we got the maximum speed of a
hydrogen atom can move before its proton and electron
fly apart is 51 027 m/s, which is much lower than the
speed of light in vacuum space.
Figure 1 shows the dependence of this speed thresh-
old on the main quantum number. It is found that with
the main quantum number increasing, the speed thresh-
old decreases, which can be fitted as f~1/n. More gener-
ally, this dependence of speed threshold on the main
quantum number can be expressed as f~k/n, where k is a
constant. This result is consistent with the fact that the
electron in outer shell of atom is easy to lose during the
Figure 1. The dependence of the speed threshold on main
quantum number.
acceleration of hydrogen atom.
Practically, in most cases, the v' can’t be zero, the
proton and electron will continue to move after they fly
apart. Figure 2 shows the dependence of the speed of
proton and electron just after they fly apart on v. It is
noticed that the speed of threshold doesn’t increase line-
arly with the final speed of proton and electron but at the
beginning, the speed of threshold increase very slowly
when the final speed of proton and electron increase. The
reason why this situation occurred is due to the fact that
the electron has angular momentum when it rotates
around proton called orbital angular momentum. The
increase of the final speeds of proton and electron at the
beginning comes from the release of the orbital angular
momentum. With the main quantum number increasing,
this situation becomes weaker and weaker, correspond-
ing to the smaller and smaller the orbital angular mo-
mentum.
Our work here first time demonstrated that the atom
can be broken into its parts by just accelerating it. Most
of people know that the electron can be removed from
atom by radiation or colliding/bombarding by atom,
electron and proton, but few people know that the same
process can be realized by just accelerating the atom to
or above its speed threshold revealed above.
Since Einstein setup relativity theory, a lot of people
dream some day they can travel with the speed of light,
therefore, they can live longer. Unfortunately, our work
here makes their dream broken. For example, we have
two inertia frames, frame a at rest but frame b moves
with speed of 0.5c. There is a hydrogen atom at rest in
frame a. Now we hope to bring this hydrogen atom from
frame a to frame b, then we have to accelerate this hy-
drogen atom at least up to 0.5c first. Based on our work
here, before the hydrogen atom reaches the speed of
frame b (0.5c), the hydrogen atom will be broken into
proton and electron when its speed reaches 51 027 m/s,
therefore, we start with a hydrogen atom from frame a
but get a free proton and a free electron in frame b in-
stead. In frame b, the proton and electron have a chance
to recombine together to form a hydrogen atom, and at
the same time, give up the energy in frame b. This proc-
ess will be the same when we try to bring a hydrogen
atom at rest in frame b to frame a. For a proton and elec-
tron to recombine into hydrog en atom, the probability of
this process depends on the concentration of proton and
electron, and relative speed of proton and electron. For a
person, if he/she is broken into parts, the probability for
him/her to be reinstalled back to him/her is definitely too
low to happen. Maybe one thinks to accelerate the hy-
drogen atom slowly enough to avoid the proton and elec-
tron in hydrogen atom to fly apart. In fact, it is impossi
ble because based on our result above, as long as the

W. X. XU 38
Figure 2. The dependence of the speed threshold on the final speed of proton/electron (just flying apart; main quantum num-
ber 1 - 10).

W. X. XU
39
speed of hydrogen atom reaches the speed threshold, the
proton and electron in hydrogen atom will fly apart
(Figure 3 the velocity corresponding to different accel-
eration). Lawrence invariance of transformation law is
still valid and all physical laws are kept the same in bo th
frames but the process from the frame a to the frame b is
not always invariance except that the difference in speed
between frame a and frame b is much lower than the
speed threshold. Our work here really a bad news for
those to dream some day they can make a time travel and
live longer but it is good news for us to develop new
technology to study the structure of matter based on our
work here. Our work also opens a way to calculate the
activation energy for the molecules in chemical reaction
and predict the reaction mechanism.
3. Light Absorption of Hydrogen Atom in
Moving
For the light absorption of hydrogen atom in moving, we
consider two processes here.
Process a.
~~~~ ~~~~~~~~~h atomatom



(v) (v')
The momentum conservation:
44
00'00'
2222 2222
10 20
88
ne ne
eh e
mmvmmv
c
nhc nhc
 



 


(12)
The energy conservation:
44
00 2'00 2
2222 2222
10 20
88
ne ne
ee
mm chmm c
nhc nhc




 


(13)
(13) c
44
00 '00
2222 2222
10 20
88
ne ne
eh e
mm cmm c
c
nhc nhc
 



 


(14)
(12) − (14)

44
00'00 '
2222 2222
10 20
()
88
ne ne
ee
mmvc mmvc
nhc nhc




 


(15)
(15) c
44'
00 '00
2222 2222
10 20
11
88
ne ne
ev ev
mm mm
cc nhc nhc



 


 

 

(16)
44'
00 00
2222 2222
2'2
10 20
22
11
11
88
11
ne ne
ev ev
mm mm
cc nhc nhc
vv
cc






 

 


(17)
44'
00 00
2222 2222
''
10 20
11
11
88
(1 )(1)(1 )(1 )
ne ne
ev ev
mm mm
cc
nhc nhc
vv vv
cc cc


 



 
 


 
 
 
(18)
'
44
00 00
2222 2222
'
10 20
11
88
11
ne ne
vv
ee
cc
mm mm
nhc nhc
vv
cc





 



(19)
'
12
'
11
11
vv
cc
QQ
vv
cc



, where4
00
12222
10
8
ne e
Qmmnhc






and 4
00
22222
20
8
ne e
Qmmnhc






(20)

W. X. XU 40
Figure 3. Velocity corresponding on different acceleration
(a : 10; 20; 30 meter per square second).
Make rearrangement, we get,
''
22
12
''
22
12
11
11
vv
QQ
cc
v
cvv
QQ
cc

 



 


(21)
Generally, v' increases with v (Figure 4). but if we
check 'vvv , it is found that vexhibits up and
down dependence on v’or v. This up and down variation
of vcomes from the electron orbital angular momen-
tum release during the excitation. This fact tells us that
when we accelerate the hydrogen atom, the hydrogen
atom speed can’t linearly increase or decrease. This re-
sult is consistent with the discussion about the depend-
ence of the speed threshold on the main quantum number
in previous paragraph.
From Equation (13), we can get,

2
'21
c
QQ
h
   (22)
In fact, we can simplify the Equation (22) by taking
'2
'
2
12
v
c
  and 2
2
12
v
c
  (23)
We get,
2'2 2
212 1
1
() ()
2
c
QQQv Qv
hh
  (24)
First term in Equation (24) is the fundamental fre-
quency during excitation. The second term in Equation
(24) is the frequency shift due to the movement of hy-
drogen atom during the excitation. It is obvious that this
frequency shift depends on both the speed of v and v'.
here exists the possibility that in some case, if initial
state of hydrogen atom or final state of hydrogen atom
involved in some other process, such as chemical reac-
tion or just collision and therefore, the v and v' be
changed, then the frequency shift term in Equation (24)
may change sign, that is, may change from blue shift to
red shit or vice versa. If this situation really happened
in our universe, then the red shift observation from the
sky is not enough for us to conclude our universe in
expansion, at least we have to make clear no other
process involved in this red shift as we discussed above.
Table 1 lists th e frequenc y shift (b lue shift) for proc-
ess a. This blue shift increases with the speed of v and
v'. But we do find if v' = 0, then we observed the red
shif t ins t e ad of b lu e shift.
Process b:
~~~~ ~~~~~~~~~~atomh atom



(v) (v')
Now we consider the process b. Based on the similar
procedure above, we get,
''
22
21
''
22
21
11
11
vv
QQ
cc
v
cvv
QQ
cc








(25)
For the process b, it is different from the process a in
that the v' is always smaller than v, not like in process a,
v' always higher than v. But the  = v'–v dependence
on v or v' is also up and down ( Figure 5 ). The reason for

v = v'–v up and down with v o r v' is th e same as in the
process a (Figure 4 ).
Similarly, we can get the frequency for the process b,


2'2 2
2121
1
2
c
QQQv Qv
hh
  (26)
The first term in Equation (26) is th e fundamental fre-
quency, the second term determines the frequency shift
(Table 2). As in process a, this frequency shift for proc-
ess b also depends on both v and v'. That means if the
initial or final state of hydrogen atom during excitation
involved in different process which causes the v or v'
Table 1. The frequency shift for process a (n1---->n2; fun-
damental frequency: 2.441 506 795 × 1015 s–1)
V(m/s) V' (m/s) Frequency Shift (s–1)
–3.22 0 –13 130 646
46.84 50 386 41 422
96.90 100 769 398 085
196.88 200 1 560 293 149
296.86 300 2 360 742 859
496.82 500 3 991 647 651
996.88 1000 7 859 519 504
1996.84 2000 1.594 573 12 × 1010
2996.79 3000 2.424 671 811×1010
3996.90 4000 3.124 430 618 × 1010
4996.86 5000 3.958 820 247 × 1010
5996.82 6000 4.815 233 973 × 1010
6996.77 7000 5.693 113 276 × 1010
7996.88 8000 6.288 723 844 × 1010
8996.84 9000 7.170 373 014 × 1010
9996.80 10 000 8.074 555 981 × 1010

W. X. XU
41
Figure 4. The relation between v, v' and v'–v for process a.
Figure 5. The relation between v, v' and v'–v for process b.
changed, then the frequency shift may change sign as we
discussed in process a. Therefore, we can’t uniquely con-clude the hydrogen atom moving away or toward us just based on the frequency shi ft o bser vati o n.

W. X. XU 42
Table 2. The frequency shift for process b (n1---->n2; fun-
damental frequency: 2.441 506 795 × 1015 s−1).
v(m/s) v' (m/s) Frequency Shift (s–1)
3.22 0 –13,130,646
53.28 50 –429,149,114
103.35 100 –861,574,263
203.33 200 –1,699,219,374
303.31 300 –2,527,310,064
503.27 500 –4,153,467,966
1003.33 1000 –8,430,721,454
2003.28 2000 –1.663229962 × 1010
3003.24 3000 –2.461910336 × 1010
4003.35 4000 –3.391175542 × 1010
5003.31 5000 –4.185565845 × 1010
6003.27 6000 –4.957931183 × 1010
7003.22 7000 –5.708830943 × 1010
8003.33 8000 –6.742244456 × 1010
9003.29 9000 –7.489375187 × 1010
10 003.25 10 000 –8.213981327 × 1010
In summary, we determined the speed threshold of
hydrogen atom and find this speed threshold depends on
both the main quantum number and the speed of final
state of proton and electron. We also calculate the fre-
quency shift due to the movement of the hydrogen atom
during its excitation. Our work here reveals that the fre-
quency shift depends on both the speed of initial and
final state of hydrogen atom. Most importantly, in some
cases, the frequency shift may change sign, which may
find application in spectroscopy analysis and new tech-
nology may be developed.
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