To determine the value that \(E = \Delta m c^2\) is used to find, let's break down the equation and what each term represents:
1. \(E\) represents energy.
2. \(\Delta m\) (delta m) represents the mass defect, which is the difference in mass resulting from a nuclear reaction.
3. \(c\) is the speed of light in a vacuum, which is a constant value of approximately \(3 \times 10^8\) meters per second.
Now, let’s interpret the context in which this equation is most commonly used:
- \(E = \Delta m c^2\) is famously known as Einstein's mass-energy equivalence formula.
- The equation tells us that a small amount of mass (\(\Delta m\)) can be converted into a large amount of energy (\(E\)) due to the multiplication by \(c^2\), where \(c\) is the speed of light, a very large number.
Given the context of the equation and its terms:
A. The energy that is released in a nuclear reaction: This option is closely related to the use of the mass-energy equivalence formula, as the equation calculates the energy (\(E\)) resulting from the mass defect (\(\Delta m\)). In nuclear reactions, such as fusion or fission, a small amount of mass is converted into a large amount of energy.
B. The mass defect: The equation involves the mass defect (\(\Delta m\)), but it does not directly find \(\Delta m\); rather, it uses \(\Delta m\) to find energy (\(E\)).
C. The mass that is lost in a fusion reaction: Similar to option B, the mass that is lost (mass defect) is part of the equation, but the primary purpose of the equation is to find the energy released.
D. The potential energy of an object raised to a certain height: This is related to gravitational potential energy described by \(E_p = mgh\), which is not what \(E = \Delta m c^2\) calculates.
E. The speed of light: The speed of light (\(c\)) is a constant in the equation, but the equation is used to calculate energy, not the speed of light itself.
Given the analysis above, the correct answer is:
A. the energy that is released in a nuclear reaction
