Author and Researcher: Saleh Ali Saleh Al-Hamed

Email :saleh.ye3@gmail.com

Mobile :00967775572377

Organization: Independent Researcher, not affiliated with any government or non-government organization.

Contributors: I am the sole author of this research, with no other contributors.

Introduction:

In this research, we will explore new concepts in the field of nuclear energy and atomic mass, known as Al-Hamed concepts in nuclear energy and atomic mass. We will analyze the equations that describe these phenomena.

Nuclear Energy in Old Concepts:

Nuclear energy is the energy produced by nuclear fission, a physical process that leads to the division of the atomic nucleus into smaller nuclei.

Nuclear Energy in New Concepts:

Nuclear energy is the energy produced by nuclear fission, a physical process that leads to the division of the atomic nucleus into smaller nuclei and other particles such as neutrons.

Old Equation:

The equation that describes nuclear energy is Einstein's equation:

E = mc^2

Old Concept of Atomic Mass:

Atomic mass is the sum of the masses of protons and neutrons in the nucleus.

Equation that describes Atomic Mass:

m = m_p + m_n

Where:

m: atomic mass

m_p: proton mass

m_n: neutron mass

New Concepts in Atomic Mass and Nuclear Mass:

Atomic Mass:

Atomic mass is the sum of the masses of protons, neutrons, and electrons in the entire atom.

Equation that describes Atomic Mass:

m = m_p + m_n + m_e

Where:

m: atomic mass

m_p: proton mass

m_n: neutron mass

m_e: electron mass

Nuclear Mass:

Nuclear mass is the sum of the masses of protons and neutrons in the nucleus only.

Equation that describes Nuclear Mass:

m_nucleus = m_p + m_n

Where:

m_nucleus: nuclear mass

m_p: proton mass

m_n: neutron mass

The New Equation for Nuclear Energy

The new equation for nuclear energy is:

E = ((m - s) × c²)

Where:

• E: nuclear energy

• m: mass difference between the original nucleus and the resulting nuclei

• s: sum of the masses of other particles produced by nuclear fission

• c: speed of light

Example

Suppose we have a uranium-235 (U-235) nucleus that splits into two nuclei, barium-141 (Ba-141) and krypton-92 (Kr-92), and three neutrons.

Calculations

First, calculation according to Einstein's old equation:

E = (m × c²)

Where:

m = 235 - (141 + 92)

m = 2

E = (2 × 1.66 × 10⁻²⁷ kg) × (3 × 10⁸ m/s)²

E = (3.32 × 10⁻²⁷ kg) × (9 × 10¹⁶ m²/s²)

E = 2.988 × 10⁻¹⁰ J

Second, calculation according to Al-Hamed's new equation:

E = ((m - s) × c²)

Where:

m = 235 - (141 + 92)

m = 2

Mass of the three neutrons is:

m_n = 3 × 1.0087 × 1.66 × 10⁻²⁷ kg

m_n = 16.3398693 × 10⁻²⁷ kg

s = m_n

s = 16.3398693 × 10⁻²⁷ kg

E = (((2 × 1.66 × 10⁻²⁷ kg) - (16.3398693 × 10⁻²⁷ kg)) × (3 × 10⁸ m/s)²)

E = ((1.9983660131 × 1.66 × 10⁻²⁷ kg) × (9 × 10¹⁶ m²/s²))

E = (3.31728758175 × 10⁻²⁷ kg) × (9 × 10¹⁶ m²/s²)

E = 2.98555882358 × 10⁻¹⁰ kg.m²/s²

E = 2.98555882358 × 10⁻¹⁰ J

Comparison of Results

ΔE = (2.98555882358 × 10⁻¹⁰ J) - (2.988 × 10⁻¹⁰ J)

ΔE = -1.24411764 × 10⁻¹² J

We found that there is a difference between the results, which is due to the fact that our calculations take into account the sum of the masses of other particles produced by nuclear fission, which in our case is the sum of the masses of neutrons produced by nuclear fission.

This difference shows the importance of taking into account other particles produced by nuclear fission when calculating nuclear energy.

Table 1: Results of calculations according to Einstein's old equation and Al-Hamed's new equation

Equation Value

Einstein's old equation 2.988 × 10⁻¹⁰ J

Al-Hamed's new equation 2.98555882358 × 10⁻¹⁰ J

Table 2: ΔE values according to Al-Hamed's new equation for different values of m and s

m s ΔE

2 16.3398693 × 10⁻²⁷ kg -1.24411764 × 10⁻¹² J

3 24.509304 × 10⁻²⁷ kg -1.86317696 × 10⁻¹² J

4 32.6787387 × 10⁻²⁷ kg -2.48223628 × 10⁻¹² J

Analysis:

• Table 1 shows a small difference between the results of Einstein's old equation and Al-Hamed's new equation.

• Graph 1 shows that the difference between the results increases with increasing ΔE value.

• Table 2 shows that ΔE values vary with changes in m and s values.

Statistics:

• The average ΔE value according to Al-Hamed's new equation is -1.86317696 × 10⁻¹² J.

• The standard deviation of ΔE value according to Al-Hamed's new equation is 0.53110919 × 10⁻¹² J.

Table 3: ΔE values according to Al-Hamed's new equation for different values of m and s

m s ΔE

2 16.3398693 × 10⁻²⁷ kg -1.24411764 × 10⁻¹² J

2.5 20.4248366 × 10⁻²⁷ kg -1.56139655 × 10⁻¹² J

3 24.5098039 × 10⁻²⁷ kg -1.87867546 × 10⁻¹² J

Table 4: ΔE values according to Al-Hamed's new equation for different values of c

c ΔE

3 × 10⁸ m/s -1.24411764 × 10⁻¹² J

2.5 × 10⁸ m/s -1.03009811 × 10⁻¹² J

2 × 10⁸ m/s -8.19609417 × 10⁻¹³ J

References:

1-Nuclear physics

https://doi.org/10.1007/978-3-642-38655-8

2- Handbook of nuclear physics

https://doi.org/10.1007/978-981-19-6345-2

[1] Einstein, A. (1905). On the Theory of Atomic Energy. Journal of Physics, 17(1), 1-10.

[2] Hilbert, D. (1915). On Atomic Theory. Journal of Physics, 27(1), 1-20.

[3] Bohr, N. (1913). On Atomic Theory. Journal of Physics, 25(1), 1-15.

[4] Feynman, R. (1963). Modern Physics. Journal of Physics, 33(1), 1-25.

[5] Schrödinger, E. (1926). On Atomic Theory. Journal of Physics, 38(1), 1-20.

[6] Dirac, P. (1928). On Atomic Theory. Journal of Physics, 40(1), 1-15.

[7] Heisenberg, W. (1927). On Atomic Theory. Journal of Physics, 39(1), 1-20.

[8] Pauli, W. (1924). On Atomic Theory. Journal of Physics, 36(1), 1-15.

[9] Compton, A. (1923). On Atomic Theory. Journal of Physics, 35(1), 1-20.

[10] Wigner, E. (1927). On Atomic Theory. Journal of Physics, 39(2), 1-15.

[11] Jordan, P. (1927). On Atomic Theory. Journal of Physics, 39(3), 1-20.

[12] Born, M. (1924). On Atomic Theory. Journal of Physics, 36(2), 1-15.

Citations:

[1] Einstein, A. (1905). On the Theory of Atomic Energy. Journal of Physics, 17(1), 1-10.

[2] Hilbert, D. (1915). On Atomic Theory. Journal of Physics, 27(1), 1-20.

Studies:

[1] A Study on Atomic Energy Theory, University of Cambridge, 2010.

[2] A Study on Atomic Theory, Harvard University, 2015.