feat: Add mass energy equivalence in physics and doctests (#10202)

* updating DIRECTORY.md

* feat: Add mass energy equivalence in physics

* updating DIRECTORY.md

* updating DIRECTORY.md

* Apply suggestions from code review

* Update physics/mass_energy_equivalence.py

* Update mass_energy_equivalence.py

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

DIRECTORY.md

@@ -815,6 +815,7 @@
   * [Kinetic Energy](physics/kinetic_energy.py)
   * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py)
   * [Malus Law](physics/malus_law.py)
+  * [Mass Energy Equivalence](physics/mass_energy_equivalence.py)
   * [Mirror Formulae](physics/mirror_formulae.py)
   * [N Body Simulation](physics/n_body_simulation.py)
   * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py)

physics/mass_energy_equivalence.py

@@ -0,0 +1,77 @@
+"""
+Title:
+Finding the energy equivalence of mass and mass equivalence of energy
+by Einstein's equation.
+
+Description:
+Einstein's mass-energy equivalence is a pivotal concept in theoretical physics.
+It asserts that energy (E) and mass (m) are directly related by the speed of
+light in vacuum (c) squared, as described in the equation E = mc². This means that
+mass and energy are interchangeable; a mass increase corresponds to an energy increase,
+and vice versa. This principle has profound implications in nuclear reactions,
+explaining the release of immense energy from minuscule changes in atomic nuclei.
+
+Equations:
+E = mc² and m = E/c², where m is mass, E is Energy, c is speed of light in vacuum.
+
+Reference:
+https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
+"""
+
+from scipy.constants import c  # speed of light in vacuum (299792458 m/s)
+
+
+def energy_from_mass(mass: float) -> float:
+    """
+    Calculates the Energy equivalence of the Mass using E = mc²
+    in SI units J from Mass in kg.
+
+    mass (float): Mass of body.
+
+    Usage example:
+    >>> energy_from_mass(124.56)
+    1.11948945063458e+19
+    >>> energy_from_mass(320)
+    2.8760165719578165e+19
+    >>> energy_from_mass(0)
+    0.0
+    >>> energy_from_mass(-967.9)
+    Traceback (most recent call last):
+        ...
+    ValueError: Mass can't be negative.
+
+    """
+    if mass < 0:
+        raise ValueError("Mass can't be negative.")
+    return mass * c**2
+
+
+def mass_from_energy(energy: float) -> float:
+    """
+    Calculates the Mass equivalence of the Energy using m = E/c²
+    in SI units kg from Energy in J.
+
+    energy (float): Mass of body.
+
+    Usage example:
+    >>> mass_from_energy(124.56)
+    1.3859169098203872e-15
+    >>> mass_from_energy(320)
+    3.560480179371579e-15
+    >>> mass_from_energy(0)
+    0.0
+    >>> mass_from_energy(-967.9)
+    Traceback (most recent call last):
+        ...
+    ValueError: Energy can't be negative.
+
+    """
+    if energy < 0:
+        raise ValueError("Energy can't be negative.")
+    return energy / c**2
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()