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 2.4:4 find the kinetic energy of the alpha particle
To find the kinetic energy of the alpha particle (He), we need to know the masses of both Thorium (Th) and the alpha particle, as well as the total energy released in the reaction.
Given that the ratio of the masses Th to He is 2.4:4, we can write this as:
Mass of Th / Mass of He = 2.4 / 4
To find the actual masses, we can assign a value to one of them. Let's assume the mass of Thorium (Th) is 2.4 units.
Therefore, Mass of He = (2.4 / 4) * Mass of Th
Next, we have the energy released in the reaction, which is given as 6.88 * 10^(-13) J.
Now we can calculate the kinetic energy of the alpha particle (He). The total energy released is distributed between the Thorium (Th) and the alpha particle (He). According to the law of conservation of energy, the sum of the kinetic energies of the products should equal the total energy released.
Kinetic energy of He + Kinetic energy of Th = Total energy released
We know the ratio of the masses Th to He, so we can assume that the kinetic energy of Th, when divided by the kinetic energy of He, will give the inverse ratio:
(Kinetic energy of Th) / (Kinetic energy of He) = 4 / 2.4
Simplifying this ratio, we get:
(Kinetic energy of Th) / (Kinetic energy of He) = 10 / 6
Now we can set up an equation using the assumption we made earlier (Mass of Th = 2.4 units):
(1/2) * (Mass of Th) * (Velocity of Th)^2 / (1/2) * (Mass of He) * (Velocity of He)^2 = 10 / 6
Cancelling out the common terms, we get:
(Mass of Th) * (Velocity of Th)^2 / (Mass of He) * (Velocity of He)^2 = 10 / 6
Substituting the values we calculated earlier:
(2.4) * (Velocity of Th)^2 / [(2.4 / 4) * Mass of Th] * (Velocity of He)^2 = 10 / 6
Now, solving for the desired quantity, the kinetic energy of the alpha particle (He), which is given as:
Kinetic energy of He = (1/2) * (Mass of He) * (Velocity of He)^2
By plugging in the calculated values, we can find the answer.
This is a general procedure for solving such problems. It involves establishing ratios between masses, equating the kinetic energies, and solving for the desired quantity using algebraic manipulation.