One of the waste products of a nuclear reactor is plutonium-239 (239_Pu). This n

Question

One of the waste products of a nuclear reactor is plutonium-239 (239_Pu). This nucleus is radioactive and decays by splitting into a hclium-4 nucleus and a uranium-235 nucleus (4_He + 235_U), the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is 8.40 times 10^-13 J and is entirely converted into the kinetic energy of the helium and uranium nuclei. The mass of the helium nucleus is 6.68 times 10^-27 kg, while that of the uranium is 3.92 times 10^-25 kg (note that the ratio of the masses is 4 to 235). Calculate the speed of the He, in meters per second, assuming the plutonium nucleus is originally at rest Calculate the speed of the U, in meters per second, assuming the plutonium nucleus is originally at rest. How much kinetic energy, in joules, does the He nucleus carry away?

Explanation / Answer

Here,

let the speed of the He atom is u1

speed of Uranium atom is u2

part a)

Using conservation of momentum

6.68 *10^-27 * u1 - 3.92 *10^-25 * u2 = 0 ----(1)

for energy

0.5 * 6.68 *10^-27 * u1^2 + 0.5 * 3.92 *10^-25 * u2^2 = 8.4 *10^-13 ----(2)

solving 1 and 2

u1 = 1.572 *10^7 m/s

u2 = 2.68 *10^5 m/s

the speed of He atoms will be 1.572 *10^7 m/s

part b)

the speed of U is 2.68 *10^5 m/s

part c)

the kinetic energy of He = 0.5 * m * u1^2

kinetic energy of He = 0.5 * 6.68 *10^-27 * (1.572 *10^7)^2

kinetic energy of He = 8.253 *10^13 J

thee kinetic energy of He is 8.253 *10^13 J

part d)

kinetic energy of U = 0.5 * m * u2^2

kinetic energy of U = 0.5 * 3.92 *10^-25 * (2.68 *10^5)^2

kinetic energy of U = 1.41 *10^-14 J

the kinetic energy of U is 1.41 *10^-14 J

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