Problem: One of the most worrisome 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 (4He + 235U), the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is 8.40 × 10-13 J and is entirely converted to 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).(a) Calculate the speeds of the two nuclei, assuming the plutonium nucleus is originally at rest.m/s (He)m/s (U)(b) About how much kinetic energy does each nucleus carry away?J (He)J (U)

FREE Expert Solution

Momentum:

p=mv

Kinetic energy:

K=12mv2

(a)

The plutonium atom is initially at rest.

From the conservation of momentum:

mpuvpu = mHevHe - mUvU (The particles move in opposite directions after slitting).

0 = 4vHe - 235vU Equation 1 

From the conservation of energy:

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Problem Details

One of the most worrisome 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 (4He + 235U), the latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is 8.40 × 10-13 J and is entirely converted to 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).

(a) Calculate the speeds of the two nuclei, assuming the plutonium nucleus is originally at rest.
m/s (He)
m/s (U)

(b) About how much kinetic energy does each nucleus carry away?
J (He)
J (U)

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