Calculate the energy released when 1 gram of uranium undergoes fission reaction
E=mc^2= 0.01*3E8 Joules
0.235
The energy released in a fission reaction can be calculated using the Einstein's mass-energy equivalence equation, E = mc^2, where E is the energy released, m is the mass converted, and c is the speed of light.
To calculate the energy released when 1 gram of uranium undergoes fission, we need to know the mass converted. The mass of uranium (specifically uranium-235) that undergoes fission is approximately 235.0439299 atomic mass units (u).
1 atomic mass unit (u) is equivalent to 1.66054 x 10^-27 kg.
Converting the mass of uranium to kilograms:
mass = (235.0439299 u) * (1.66054 x 10^-27 kg/u) = 3.90 x 10^-25 kg
Using the speed of light:
c = 3.00 x 10^8 m/s
Now, we can calculate the energy released:
E = (mass) * (c^2) = (3.90 x 10^-25 kg) * (3.00 x 10^8 m/s)^2
E ≈ 3.51 x 10^13 Joules
Therefore, the energy released when 1 gram of uranium undergoes fission is approximately 3.51 x 10^13 Joules.
To calculate the energy released when 1 gram of uranium undergoes a fission reaction, we need to use the equation E = mc^2, where E is the energy released, m is the mass converted, and c is the speed of light.
First, we need to determine the amount of uranium that would undergo fission. The molar mass of uranium is approximately 238 grams per mole, and the atomic mass unit (u) of uranium is 238, which means 1 mole of uranium weighs 238 grams.
Since we have 1 gram of uranium, we can use the molar mass to calculate the number of moles of uranium involved in the reaction:
Number of moles = mass / molar mass
Number of moles = 1 gram / 238 grams per mole
Number of moles ≈ 0.0042 moles
Now, we need to calculate the mass that is converted during the fission reaction. Fission typically converts only a small fraction of the uranium's mass. On average, about 0.1% of the uranium's mass is converted to energy through fission.
Mass converted = mass of uranium × conversion fraction
Mass converted = 1 gram × 0.001
Mass converted ≈ 0.001 grams
Now, we can use the equation E = mc^2 to calculate the energy released:
E = mass converted × (speed of light)^2
E = 0.001 grams × (3 × 10^8 meters per second)^2
E ≈ 9 × 10^11 joules
Therefore, when 1 gram of uranium undergoes a fission reaction, approximately 9 × 10^11 joules of energy are released.