Class I Help Due Date: 7/6/2018 Homework: Conservation of Momentum Begin Date: 6
ID: 1864002 • Letter: C
Question
Class I Help Due Date: 7/6/2018 Homework: Conservation of Momentum Begin Date: 6/4/2018 12:00:00 AM 11:59:00 PM End Date: 7/6/2018 11:59:00 PM (4%) Problem 25: One of the waste products of a nuclear reactor is plutonium-239 (239Pu) This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus He23),the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is 8.40 x 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 × 10-27 kg , while that of the uranium is 3.92 × 10-25 kg (note that the ratio of the masses is 4 to 235). 25% Part (a) Calculate the speed of the He, in meters per second, assuming the plutonium nucleus is originally at rest. Grade Summary 056 100% Potential sinO cotano asin) tan) acosO coso 4 5 6 1 2 Attempts remaining: 20 (0% per attempt) detailed view atan acotan) sinhO coshO tanh cotanh0 ODegrees Radians I give up! Hints:--deduction per hint. Hints rernaining:- Feedback:% deduction per feedback 25% Part (b) Calculate the speed of the U, in meters per second, assuming the plutonium nucleus is originally at rest -a25% Part (c) How much kinetic energy, in Joules, does the He nucleus carry away? -£ 25% Part (d) How much kinetic energy, in Joules, does the U nucleus carry away?Explanation / Answer
Suppose the speed of the He atom is u1
speed of Uranium atom is u2
a) Using law of 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
So, the speed of He atoms will be 1.572 *10^7 m/s
b) the speed of U is 2.68 *10^5 m/s
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
So, kinetic energy of He is 8.253 *10^-13 J
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
So, the kinetic energy of U is 1.41 *10^-14 J
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