What total mass must be converted into energy

to produce a gamma photon with an energy of
1.03 × 10^–13 joule

1.14×10^−20

This is the answer.

e = m c^2

1.03 * 10^-13 = m (9*10^16)
m = (1.03/9) 10^-29 kg

To determine the total mass that must be converted into energy to produce a gamma photon with an energy of 1.03 × 10^–13 joules, we can use Albert Einstein's mass-energy equivalence equation, E=mc^2. Rearranging the equation, we get m = E/c^2, where m is the mass, E is the energy, and c is the speed of light (c ≈ 3 * 10^8 m/s).

Substituting the given values into the equation:
m = (1.03 × 10^–13 J) / (3 * 10^8 m/s)^2
m = 1.03 × 10^–13 J / (9 * 10^16 m^2/s^2)
m = 1.14 × 10–30 kg

Therefore, to produce a gamma photon with an energy of 1.03 × 10^–13 joules, approximately 1.14 × 10–30 kilograms of mass must be converted into energy.

To determine the total mass that must be converted into energy to produce a gamma photon with a given energy, we can use Albert Einstein's mass-energy equivalence equation, E=mc², where E represents the energy, m represents the mass, and c represents the speed of light.

In this case, we are given the energy of the gamma photon as 1.03 × 10^–13 joules. We want to find the equivalent mass.

First, we rearrange the equation to solve for mass (m):
m = E / c²

The speed of light, c, is a constant value of approximately 3 × 10^8 meters per second.

Now we can substitute the given values into the equation:
m = (1.03 × 10^–13 joules) / (3 × 10^8 meters per second)²

To simplify the calculation, we square the speed of light:
m = (1.03 × 10^–13 joules) / (9 × 10^16 meters² per second²)

Next, divide the given energy by the squared speed of light:
m = (1.03 × 10^–13 joules) / (9 × 10^16 meters² per second²)

Now, calculate the mass:
m = 1.144 × 10^–30 kilograms

Therefore, to produce a gamma photon with an energy of 1.03 × 10^–13 joules, approximately 1.144 × 10^–30 kilograms of mass must be converted into energy.