How much energy, in megaelectronvolts, is produced when 0.250 universal mass unit of matter is completely converted into energy?
The Correct Answer and Explanation is :
To find out how much energy is produced when 0.250 universal mass unit (u) of matter is completely converted into energy, we can use Einstein’s famous equation:
[
E = mc^2
]
Where:
- (E) is the energy produced,
- (m) is the mass being converted,
- (c) is the speed of light ((3.00 \times 10^8 \, \text{m/s})).
Step 1: Convert the mass to kilograms
1 universal mass unit (u) is approximately equal to (1.660539 \times 10^{-27}) kilograms.
So, the mass of 0.250 u is:
[
m = 0.250 \, \text{u} \times 1.660539 \times 10^{-27} \, \text{kg/u}
]
[
m = 4.15135 \times 10^{-28} \, \text{kg}
]
Step 2: Apply Einstein’s equation
Now, using the equation (E = mc^2):
[
E = 4.15135 \times 10^{-28} \, \text{kg} \times (3.00 \times 10^8 \, \text{m/s})^2
]
[
E = 4.15135 \times 10^{-28} \, \text{kg} \times 9.00 \times 10^{16} \, \text{m}^2/\text{s}^2
]
[
E = 3.735 \times 10^{-11} \, \text{Joules}
]
Step 3: Convert Joules to Mega electronvolts (MeV)
1 Joule is equal to (6.242 \times 10^{12}) MeV.
So,
[
E = 3.735 \times 10^{-11} \, \text{J} \times 6.242 \times 10^{12} \, \text{MeV/J}
]
[
E = 233.5 \, \text{MeV}
]
Final Answer:
The energy produced when 0.250 universal mass units of matter is completely converted into energy is approximately 233.5 MeV.
This calculation demonstrates the enormous amount of energy released in mass-energy conversion, illustrating the power of Einstein’s theory in explaining nuclear reactions and particle physics.