Energy is released during a nuclear reaction

due to a conversion between mass and energy.
Mass is not conserved. The initial and final
amounts are different.
If a total of 4.6 g of mass were “missing”,
how much energy is released? The speed of
light is 3 × 108 m/s.
Answer in units of J

E=mc²

To determine how much energy is released during a nuclear reaction when 4.6 g of mass is "missing," we need to use Einstein's famous equation: E = mc^2.

Here's a step-by-step guide on how to calculate the energy released:

Step 1: Convert the missing mass from grams to kilograms.
4.6 g = 4.6 x 10^(-3) kg (since there are 1000 grams in a kilogram)

Step 2: Plug the value of mass (m) into the formula E = mc^2.
E = (4.6 x 10^(-3) kg) x (3 x 10^8 m/s)^2

Step 3: Calculate the square of the speed of light.
(3 x 10^8 m/s)^2 = 9 x 10^16 m^2/s^2

Step 4: Multiply the mass and the square of the speed of light to find the energy.
E = (4.6 x 10^(-3) kg) x (9 x 10^16 m^2/s^2)

Step 5: Simplify the expression.
E = 4.14 x 10^14 kg m^2/s^2

Step 6: Finally, convert the unit of energy from kg m^2/s^2 to joules (J).
1 J = 1 kg m^2/s^2, so E = 4.14 x 10^14 J

Therefore, the amount of energy released during the nuclear reaction when 4.6 g of mass is "missing" is approximately 4.14 x 10^14 joules (J).