Question

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then,

the helium nucleus has more kinetic energy than the thorium nucleus

the helium nucleus has less momentum than the thorium nucleus

the helium nucleus has more momentum than the thorium nucleus

the helium nucleus has less kinetic energy than the thorium nucleus

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Solution

the helium nucleus has more kinetic energy than the thorium nucleus

straight U presubscript 92 superscript 238 space rightwards arrow Th presubscript 90 superscript 238 space plus space He presubscript 2 superscript 4 According space to space law space of space consevation space of space linear space momentum comma space we space have vertical line straight P subscript Th vertical line space equals space vertical line straight P subscript He vertical line rightwards double arrow space As comma space kinetic space energy space of space an space element KE space equals fraction numerator straight P squared over denominator 2 straight m end fraction where space straight m comma space is space mass space of space an space element space Thus comma space KE space proportional to space 1 over straight M So comma space straight M subscript He space less than space straight M subscript Th space rightwards double arrow space straight K subscript He space greater than space straight K subscript Th

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