In the reaction U gives Th + He 6.88*10-13 J energy are released as the kinetic energies of the products. If the ratios of the masses Th to He is 234:4 find the kinetic energy of the alpha particle
To find the kinetic energy of the alpha particle (He), we first need to calculate the total energy released in the reaction. Given that the energy released is 6.88 * 10^-13 J, we can use this information to find the mass difference between uranium (U) and thorium (Th).
1. Energy released per reaction:
Energy released = 6.88 * 10^-13 J
2. Mass difference between U and Th:
The mass difference can be calculated using Einstein's mass-energy equivalence equation: E = mc^2
Where E is the energy released, m is the mass difference, and c is the speed of light.
Rearranging the equation to solve for mass difference:
m = E / c^2
Plugging in the given values:
m = (6.88 * 10^-13 J) / (3 * 10^8 m/s)^2
3. Ratio of masses:
The ratio of masses between Th and He is given as 234:4, which means 1 Th atom has a mass 234 times larger than 1 He atom.
4. Calculate the mass of He (alpha particle):
The mass difference between U and Th represents the mass of Th that is converted into energy. So, the mass difference is the mass of Th minus the mass of He.
Let the mass of Th be represented as x (so the mass of He is x/234):
m = x - (x/234)
5. Solve for x (mass of Th):
Substitute the mass difference (m) calculated in step 2 into the equation from step 4:
(6.88 * 10^-13 J) / (3 * 10^8 m/s)^2 = x - (x/234)
Solve for x using this equation.
6. Calculate the mass of He (alpha particle):
Once you have obtained the value of x, substitute it back into the equation from step 4 to find the mass of He (x/234).
7. Calculate the kinetic energy of the alpha particle (He):
Finally, to find the kinetic energy of the alpha particle, you can use the equation for kinetic energy:
KE = (1/2) * m * v^2
Where m is the mass of He and v is the velocity of He in meters per second (can be assumed to be the speed of light, c).
Substitute the calculated mass of He and the value of c into the equation to find the kinetic energy of the alpha particle.