Question

The mass of a carbon atom is 12.00 amu while the mass of a helium-4 atom is 4.003 amu. If a gamma ray photon splits a carbon atom into three Helium atoms, how much energy is converted into mass?

Answer 1

The energy converted into mass when a gamma ray photon splits a carbon atom into three helium atoms is -4.14 × 10^-11 J.

Step-by-step explanation:

The mass difference between the carbon atom and the three helium atoms is 12.00 amu - 3(4.003 amu) = -0.009 amu. This mass difference is converted into energy.

To calculate the amount of energy converted, we can use Einstein's equation, E=mc^2, where E is the energy, m is the mass difference, and c is the speed of light.

Plugging in the values, we have E=(-0.009 amu)(c^2). To convert amu to kilograms, we use the conversion factor 1 amu = 1.66 × 10^-27 kg. Therefore, the energy converted is (-0.009 amu)(1.66 × 10^-27 kg/amu)(3 × 10^8 m/s)^2 = -4.14 × 10^-11 J.