search
top

The Quantisation of Distance



The Quantisation of Distance

When you are inter­ested in physics you must read “Unbe­liev­able”!

Bohr’s Cor­re­spon­dence Prin­ci­ple sug­gests that equa­tions (5a) and (6) are the same and they appear to be so. Because the energy lev­els of atoms are dis­crete, quan­ti­fied, one can pre­sume that the dis­tance is quan­ti­fied in some way because the spe­cific energy quan­ti­sa­tion of the atom must coin­cide with cer­tain dis­crete leaps in orbit­ing dis­tance. Despite the energy quan­tifi­ca­tion with n by QM clas­si­cal EM-​physics still deter­mines that the increas­ing quan­tum level n has to coin­cide with cor­re­spond­ing increase of orbit dis­tances accord­ing to the con­ser­va­tion law of energy.

The equa­tions for the energy level of the atom accord­ing to Bohr’s model (6) and the EM-​equation (5a) can be seen as iden­ti­cal. We can express the quan­tum energy lev­els of the hydro­gen atom ade­quately with:

(9)

where the radius RBohr is the radius of the hydro­gen atom accord­ing to Bohr (n=1) and n the prin­ci­pal quan­tum number.

The dis­tance of the elec­tron to the nucleus is the macro-​world fac­tor that deter­mines the energy level of the atom and also deter­mines the energy level of Bohr’s atomic model. The quan­tum num­ber n indi­cates that for the quan­tum dis­tances Rn, for n=1,2,3… the sta­ble ion­iza­tion energy lev­els are observed.

Because equa­tion (6) is iden­ti­cal to equa­tion (5a) when we derive equation:

(10)

Rn is the orbit dis­tance of the elec­tron in the Bohr-​hydrogen atom. The clas­si­cal Compton-​radius Rc of the elec­tron is cal­cu­lated accord­ing to the equation:

Exactly the same radius for the elec­tron is derived in chap­ter “The Elec­tron” in “From Para­dox to Par­a­digm” where the rest mass/​energy of the elec­tron is calculated:

where the first part of the equa­tion is the elec­tro­sta­tic energy and the sec­ond part the dynamic spin-​energy of the electron.

Sub­sti­tu­tion of Me in (10) and con­sid­er­ing we find:

(10a)

for n=1 the radius of orbit is the Bohr-​radius of the hydro­gen atom. We cal­cu­late the ratio:

The dis­tance ratio between the last energy trap in the atom , the rydberg-​distance, and the first, the Bohr-​distance, is expressed with ratio (the quan­tum num­ber ):

(11) ***

With equa­tion (8) we cal­cu­lated that the ryd­berg prin­ci­pal quan­tum num­ber is . The prin­ci­pal quan­tum num­ber can also be expressed gen­er­ally with the ratio:

The dif­fer­ence between (8a) and (8) is that the quan­tum num­ber N is cal­cu­lated dif­fer­ently. We will show that the ryd­berg dis­tance is

and that there are there­fore ion­iza­tion lev­els and that

Next chap­ter: The Planck-​radius

When you are interested in physics you must read “Unbelievable“!

Bohr’s Correspondence Principle suggests that equations (5a) and (6) are the same and they appear to be so. Because the energy levels of atoms are discrete, quantified, one can presume that the distance is quantified in some way because the specific energy quantisation of the atom must coincide with certain discrete leaps in orbiting distance. Despite the energy quantification with n by QM classical EM-physics still determines that the increasing quantum level n has to coincide with corresponding increase of orbit distances according to the conservation law of energy.

The equations for the energy level of the atom according to Bohr’s model (6) and the EM-equation (5a) can be seen as identical. We can express the quantum energy levels of the hydrogen atom adequately with:

 (9)

where the radius RBohr is the radius of the hydrogen atom according to Bohr (n=1) and n the principal quantum number.

The distance  of the electron to the nucleus is the macro-world factor that  determines the energy level of the atom and also determines the energy level of Bohr’s atomic model. The quantum number n indicates that for the quantum distances Rn, for n=1,2,3…  the stable ionization energy levels are observed.

Because equation (6) is identical to equation (5a) when we derive equation:

    (10)

Rn is the orbit distance of the electron in the Bohr-hydrogen atom. The classical Compton-radius Rc of the electron is calculated according to the equation:

Exactly the same radius for the electron is derived in chapter “The Electron” in “From Paradox to Paradigm” where the rest mass/energy of the electron is calculated:

where the first part of the equation is the electrostatic energy and the second part the dynamic spin-energy of the electron.

Substitution of Me in (10) and considering we find:

(10a)

for n=1 the radius of orbit is the Bohr-radius of the hydrogen atom. We calculate the ratio:   

The distance ratio between the last energy trap in the atom , the rydberg-distance, and the first, the Bohr-distance, is expressed with ratio (the quantum number ):

 (11)  ***

With equation (8) we calculated that the rydberg principal quantum number is . The principal quantum number can also be expressed generally with the ratio:

The difference between (8a) and (8) is that the quantum number N is calculated differently. We will show that the rydberg distance is 

and that there are therefore  ionization levels and that 

Next chapter: The Planck-radius

top