A uranium-238 nucleus at rest undergoes radioactive decay, splitting into an alp

Question

A uranium-238 nucleus at rest undergoes radioactive decay, splitting into an alpha particle (helium nucleus) with mass 6.64×10-27 kg and a thorium nucleus with mass 3.89×10-25 kg. The measured kinetic energy of the alpha particle is 4.95×10-13 J.


positive x: If after the decay, the thorium nucleus is observed to move in the negative x direction. After the decay, what direction did the alpha particle move?

Complete the following statement with less than, greater than or equal to.

After the decay, the kinetic energy of the alpha particle was _________ the kinetic energy of the thorium nucleus.

Explanation / Answer

m = mass of alpha particle = 6.64 x 10-27 kg

v = speed of alpha particle = ?

KEalpha = kinetic energy of alpha particle = (0.5) m v2

4.95 x 10-13 =  (0.5) (6.64 x 10-27) v2

v = 1.22 x 107 m/s

using conservation of momentum

0 = MV + mv

0 = (3.89 x 10-25) V + (6.64 x 10-27) (- 1.22 x 107)

V = 2.1 x 105 m/s

KEthorium = kinetic enenrgy of thorium = (0.5) MV2 = (0.5) (3.89 x 10-25) (2.1 x 105)2 = 8.6 x 10-15 J

so kinetic energy of alpha particle is greater

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