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:

m_{pu}v_{pu} = m_{He}v_{He} - m_{U}v_{U} (The particles move in opposite directions after slitting).

0 = 4v_{He} - 235v_{U} Equation 1

From the conservation of energy:

One of the most worrisome waste products of a nuclear reactor is plutonium 239 (^{239}Pu). This nucleus is radioactive and decays by splitting into a helium-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 × 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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