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A NEW ATOMIC MODEL

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# Florian Ion PETRESCU^{ }^{1}

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^{1 }Chair TMR, Bucharest Polytechnic University, ROMANIA, petrescuflorian@yahoo.com

*Abstract: **This paper presents shortly a new and original relation (18) to calculate the radius with that the electron is running around the nucleus of an atom. One utilizes two times the Lorentz relation (5), the Niels Bohr generalized equation (7), and a mass relation (4) which was deduced from the kinematics energy relation written in two modes: classical (1) and coulombian (2). Equalizing the mass relation (4) with Lorentz relation (5) one obtains the equation (6), which give us a relation between the electron speed square (v*^{2}) and the radius (r). The second relation (8), between v^{2} and r, has been obtained by equalizing the mass from Bohr’s equation (7) and the mass from Lorentz’s relation (5). In the system (8) – (6) eliminating the electron speed square (v^{2}), one determines the radius r, with that, the electron is moving around the nucleus; see the relation (18). The author realizes by this a new atomic model, or a new quantum theory.

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*Key words: **Atom, atomic, electron, nucleus, quantum, radius, energy, below levels, layer, cloud. *

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** 1. Introduction**

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In this paper the author determine a new relation for calculating the radius with that the electron is running around the nucleus of an atom. In this mode the author realizes a new theoretical atomic model.

**2. The new relations **

Writing the kinematics energy relation in two ways, classical (1) and Coulombian (2) one determines the relation (3):

*E*_{C}=1/2mv^{2} (1)

*E*_{C}=Ze^{2}/(8*p**e*_{0}*r)* (2)

*mv*^{2}=Ze^{2}/(4*p**e*_{0}*r)* (3)

From equation (3), determining explicit the mass of the electron, one obtains the relation (4):

*m=Ze*^{2}/(4*p**e*_{0}*v*^{2}r) (4)

Now, we write the known relation of Lorentz (5), for the mass of a corpuscle, in function of the corpuscle speed, at the power two:

*m=m*_{0}c/RAD with RAD=(c^{2}-v^{2})^{1/2} (5)

With the relations (4) and (5) one obtains the first essential expression (relation 6):

*m*_{0}c/RAD= *Ze*^{2}/(4*p**e*_{0}*v*^{2}r) (6)

One utilizes now, the Niels Bohr generalized relation (7):

*m=n*^{2}*e*_{0}*h*^{2}/(*p**re*^{2}Z) (7)

One utilizes for the second time the Lorentz relation (5), with the Bohr relation (7) and in this mode one obtains the second essential expression (relation 8):

*m*_{0}c/RAD= n^{2}*e*_{0}*h*^{2}/(*p**re*^{2}Z) (8)

Now, on keep just the two essential expressions (the relations 6 and 8).

One writes (8) in the form (8’):

*RAD n*^{2}*e*_{0}*h*^{2}=*p**r m*_{0}c e^{2}Z (8’)

One put the form (8’) at the power two, to explicit the speed of electron at power two (v^{2}), see the equation (9):

*v*^{2}=(n^{4}*e*_{0}^{2}*h*^{4}–*p*^{2}*r*^{2}m_{0}^{2}e^{4}Z^{2})c^{2}/(n^{4}*e*_{0}^{2}*h*^{4}) (9)

The equation (9) can be written in the form (10):

*v*^{2}=c^{2}-kc^{2}r^{2} (10)

where the constant k take the form (10’):

*k=**p*^{2}*m*_{0}^{2}e^{4}Z^{2})/(n^{4}*e*_{0}^{2}*h*^{4}) (10’)

Now one writes the essential equation (6) in the form (6’):

*4m*_{0}c*p**e*_{0}rv^{2}=Ze^{2}RAD (6’)

Then, one squares the equation (6’), and obtains the relation (6’’):

*16m*_{0}^{2}c^{2}*p*^{2}*e*_{0}^{2}r^{2}v^{4}=Z^{2}e^{4}RAD (6’’)

In the relation (6’’) one introduces the squared electron speed, taken from the equation (10) and it obtains the formula (11):

*16m*_{0}^{2}*p*^{2}*e*_{0}^{2}(c^{2}-kc^{2}r^{2})^{2}=Z^{2}e^{4}k (11)

The relation (11) can be written in the form (12):

*(c*^{2}-kc^{2}r^{2})^{2}=Z^{2}e^{4}k/(16m_{0}^{2}*p*^{2}*e*_{0}^{2}*)* (12)

One squares the relation (12) and it obtains the expression (13):

*(c*^{2}-kc^{2}r^{2})=*±**Ze*^{2}k^{1/2}/(4m_{0}*p**e*_{0}*)* (13)

The relation (13) can be written in the form (14):

*kc*^{2}r^{2}= c^{2}*±**Ze*^{2}k^{1/2}/(4m_{0}*p**e*_{0}*)* (14)

One explicit the squared radius (r^{2}), from the relation (14) and one obtains the equation (15):

*r*^{2}=1/k*±**Ze*^{2}/(*4m*_{0}*p**e*_{0}*k*^{1/2}c^{2})* * (15)

Now, one exchanges, in the relation (15), the constant k with the expression (10’) and it obtains the equation (16):

*r*^{2}=n^{4}*e*_{0}^{2}*h*^{4}/(*p*^{2}*m*_{0}^{2}e^{4}Z^{2})*±**n*^{2}h^{2}/(4*p*^{2}*m*_{0}^{2}c^{2}) (16)

The expression (16) can be put in the form (17):

*r*^{2}=n^{4}*e*_{0}^{2}*h*^{4}/(*p*^{2}*m*_{0}^{2}e^{4}Z^{2}).[1*±**e*^{4}Z^{2}/(4c^{2}*e*_{0}^{2}*h*^{2}n^{2})] (17)

Extracting square root from the expression (17), one obtains for the radius (r), the final expression (18) (Physically, there is only the positive solution for r, and from the four solutions of radius r, remain only one solutions):

*r=n*^{2}*e*_{0}*h*^{2}/(*p**m*_{0}e^{2}Z).[1*–**e*^{4}Z^{2}/(4c^{2}*e*_{0}^{2}*h*^{2}n^{2})]^{1/2} (18)

**3. Notes utilized **

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The permissive (permittivity) constant:

e_{0}=8.85418*10^{-12 }[C^{2}/(Nm^{2})];

The Planck constant: h=6.626*10^{-34} [J.s];

The rest mass of electron: m_{0}=9.1091*10^{-31} [kg];

The Pythagoras’s constant: p=3.141592654;

The elementary electrical load: e=-1.6021*10^{-19} [C];

The light speed in vacuum: c=2.997925*10^{8} [m/s];

n=the principal quantum number (the Bohr quantum number);

Z=the number of protons from the atomic nucleus (the atomic number).