# 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:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

(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:

###### 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)