Question

How much energy is released in mass defect of 1 amu?

Hint:

The energy released in a mass defect is directly related to the mass using the equation \( E = \Delta m c^2 \).

Answer 1

Step 1: Formula for energy released due to mass defect.
The energy released in the mass defect is given by Einstein's equation: \[ E = \Delta m c^2 \] where \( E \) is the energy, \( \Delta m \) is the mass defect, and \( c \) is the speed of light.
Step 2: Substituting the values.
The mass defect is given as 1 amu. To convert this into kg, we use the conversion factor: \[ 1 \, \text{amu} = 1.660539 \times 10^{-27} \, \text{kg} \] The speed of light \( c \) is \( 3 \times 10^8 \, \text{m/s} \). Now, substituting these values into the formula: \[ E = 1.660539 \times 10^{-27} \times (3 \times 10^8)^2 \] \[ E = 1.660539 \times 10^{-27} \times 9 \times 10^{16} = 1.494485 \times 10^{-10} \, \text{J} \]
Step 3: Conclusion.
Therefore, the energy released due to a mass defect of 1 amu is \( 1.494485 \times 10^{-10} \, \text{J} \).