To determine which equation governs the energy produced during nuclear reactions, we need to analyze the given options and understand their contexts:
A. [tex]\(E = mgh\)[/tex]
This equation represents the gravitational potential energy of an object with mass [tex]\(m\)[/tex] at height [tex]\(h\)[/tex] in a gravitational field with acceleration due to gravity [tex]\(g\)[/tex]. This is not related to nuclear reactions.
B. [tex]\(E = mc^2\)[/tex]
This is Einstein's famous equation from his theory of relativity. It states that mass [tex]\(m\)[/tex] can be converted into energy [tex]\(E\)[/tex] equivalently, with [tex]\(c\)[/tex] being the speed of light in a vacuum. This equation directly relates to the energy produced during nuclear reactions as mass is converted to energy.
C. [tex]\(E = \frac{1}{2} mv^2\)[/tex]
This equation represents the kinetic energy of an object with mass [tex]\(m\)[/tex] moving with velocity [tex]\(v\)[/tex]. Kinetic energy is not the primary consideration in nuclear reactions.
D. [tex]\(E = hv\)[/tex]
This equation, known as Planck's equation, relates the energy [tex]\(E\)[/tex] of a photon to its frequency [tex]\(v\)[/tex] (or [tex]\(f\)[/tex]) with [tex]\(h\)[/tex] being Planck's constant. This is relevant in the context of quantum mechanics and the energy of photons, but not directly in nuclear reactions.
Upon analysis, the correct equation that governs the energy produced during nuclear reactions is:
[tex]\(E = mc^2\)[/tex]
Therefore, the equation that governs the energy produced during nuclear reactions is [tex]\(E = mc^2\)[/tex]. Given the options, this corresponds to option B.
