1. Introduction

2. Origin of the Electromagnetic Charge and Quantum of Magnetic Flux

a)

Up, Charm and Top quark’s electromagnetic charge is $+\frac{2}{3}{e}_n\cong +2e.$

b)

Down, Strange and Bottom quark’s electromagnetic charge is $-\frac{1}{3}{e}_n\cong -e.$

c)

Quarks having an electromagnetic charge of $\pm 2e$ and $\mp e$ can be called as integral charge quarks.

d)

There exists no repulsion between any two particles having same kind of nuclear charge.

3. Origin of the Planck’s Radiation Constant

4. Origin of Celestial Magnetic Moments

5. Discussion on Interaction Strength and Large gravitational Coupling Constants at Atomic Level

a)

Interaction range is inversely proportional to interaction strength.

b)

Effective magnitude of the operating gravitational constant is, $G_x\cong \frac{G_N}{\mathrm{Interaction}\mathrm{strength}}$

6. Discussion on Discreteness Associated with Quantum Nature at Atomic Level

1)

Proposed weak fermion and proposed weak gravitational constant play a key role in quantifying $\hslash c.$

2)

‘Numbering nature’ of elementary particles seems to be the root cause of origin of discreteness in microscopic physics.

3)

Discreetness of $\hslash$ can be understood with,

$$n^2.\hslash \cong \frac{G_w{\left(n.M_{wf}\right)}^2}{c}$$

(14)

where $n$ =1,2,3,.. = Number of $M_{wf}$.

4)

Based on relation (7) and considering $\left(\sqrt{G_n{m}_p},\sqrt{G_e{m}_e}\right)$as characteristic inherent constants, Bohr’s discrete angular momentum of electron [28] can be understood with,

$$n.\hslash \cong \frac{\sqrt{G_n{m}_p}\sqrt{G_e{m}_e}}{c}\times \left(n.m_e\right)$$

(15)

where $n$=1,2,3,.. = Number of electrons or number of hydrogen atoms.

7. Various Applications of the Proposed Nuclear Elementary Charge

1)

Fine structure ratio can be expressed as,

$$\alpha \cong \left(\frac{e^2}{4\pi {\epsilon }_0\hslash c}\right)\cong \sqrt{\left(\frac{e^2}{4\pi {\epsilon }_0{G}_e{m}_e^2}\right)\left(\frac{e^2}{4\pi {\epsilon }_0{G}_n{m}_p{m}_e}\right)}\cong \frac{e{e}_n}{4\pi {\epsilon }_0{G}_n{m}_p^2}$$

(16)

2)

Potential energy of electron in Bohr radius can be expressed as,

$$P.E_{Bohr}\cong -{\alpha }^2{m}^e{c}^2\cong -\left(\frac{e^2}{4\pi {\epsilon }_0{G}_n{m}_p^2}\right)\left(\frac{e_n^2}{4\pi {\epsilon }_0{G}_n{m}_p^2}\right)m^e{c}^2\cong -\left(\frac{e^2}{4\pi {\epsilon }_0{G}_e{m}_e^2}\right)\left(\frac{e^2}{4\pi {\epsilon }_0\left(G_n{m}_p/c^2\right)}\right)$$

(17)

3)

Starting form Z=40, L-alpha X-ray transition energies (Transition: L₃M₅ (L$\alpha$₁)) can be understood with a very simple relation,

$$h{\nu }_{L\alpha }\cong \left[\frac{{\left(Z-7.2\right)}^2}{7.2}\right]13.6\mathrm{eV}\mathrm{where}\frac{e_n}{e}\left(\frac{e_n}{e}-\frac{1}{2}\right)\cong \mathrm{7.2.}$$

(18)

a)

Moseley’s [29,30] nuclear charge screening factor for L-alpha X-rays is strikingly matching with $\frac{e_n}{e}\left(\frac{e_n}{e}-\frac{1}{2}\right)\cong \mathrm{7.2.}$ This can be considered as one best application of the proposed nuclear elementary charge in atomic physics.

b)

Strange coincidence is that, $\frac{e_n}{e}\left(\frac{e_n}{e}-\frac{1}{2}\right)\cong {\left(\frac{1}{2^2}-\frac{1}{3^2}\right)}^{-1}\cong \mathrm{7.2.}$ It needs further study. Solving this relation, obtained $\frac{e_n}{e}\cong \mathrm{2.944902596.}$ Considering this value, all other proposed gravitational constants can be estimated. Estimated Newtonian gravitational constant is, $G_N\cong 6.669957\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}$and error is 0.0651%. Our estimated unified value is $G_N\cong 6.679851\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}.$Average value of these two is $G_N\cong 6.674904\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\sec }^{-2}.$This value is matching with the recommended value [18]. It may be a coincidence and needs a review.

4)

As expected, by considering the proposed nuclear charge, there is a scope for understanding nuclear binding energy. For $Z\ge 3\mathrm{and}N\ge Z,$ nuclear binding energy, can be understood with a simple relation of the form [31,32],

$$BE\cong \left\{A-\left[1+\left(0.0016\left(\frac{Z^2+A^2}{2}\right)\right)\right]-A^{1/3}-\frac{{\left(A_s-A\right)}^2}{A_s}\right\}\left(B_0\cong 10.1\mathrm{MeV}\right)$$

(19)

$$\mathrm{where}\{\begin{array}{l}\mathrm{Z}=\mathrm{Proton}\mathrm{number}\\ \mathrm{A}=\mathrm{Mass}\mathrm{number}\\ A_s\cong \left(2Z\right)+0.0016{\left(2Z\right)}^2\cong 2Z+0.0064Z^2\\ =\mathrm{Estmated}\mathrm{mass}\mathrm{number}\mathrm{close}\mathrm{to}\mathrm{stable}\mathrm{mass}\mathrm{number}\\ B_0\cong \sqrt{\left(\frac{e^2}{8\pi {\epsilon }_0\left(\hslash /m_{p}c\right)}\right)\left(\frac{e_n^2}{8\pi {\epsilon }_0\left(\hslash /m_{p}c\right)}\right)}\cong \frac{e_{n}e}{8\pi {\epsilon }_0\left(\hslash /m_{p}c\right)}\cong 10.1\mathrm{MeV}\\ \mathrm{where}\hslash /m_{p}c=\mathrm{Reduced}\mathrm{Comption}\mathrm{wavelength}\mathrm{of}\mathrm{proton}.\end{array}$$

8. Conclusion

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