# 23U (atoic mass 238.050784 u) decays via alpha decay to 234Th (atomic mass 234.043593 u).What is the kinetic energy of the emitted alpha particle? Assume the uranium nucleus was initiallyat rest (so the initial momentum was zero).

Question
14 views help_outlineImage Transcriptionclose23U (atoic mass 238.050784 u) decays via alpha decay to 234Th (atomic mass 234.043593 u). What is the kinetic energy of the emitted alpha particle? Assume the uranium nucleus was initially at rest (so the initial momentum was zero). fullscreen
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Step 1

Alpha-decay of  238uranium is shown by equation (1)

Mass of uranium atom =238.0507785 u

Mass of thorium atom =234.043594 u

Mass of alpha-particles = 4.002603 u

Q-value for this reaction help_outlineImage Transcriptionclose234Th+4He 90 238U 92 (1) (2) Q-value-931.5 m,-mr MeV =-931.5(234.043594+4.002603-238.0507785) MeV = 4.274 MeV fullscreen
Step 2

It is given that the initial momentum of uranium is zero.

According to the conservation of momentum law-

As momentum  (P) = mass × velocity

Als... help_outlineImage TranscriptionclosePU PThPHe - Рrh-Pне 0 P ThHe =P Th (3) MThVть МНе'Не V. =__Th 'Th 4) "Не М, Не Kinetic energy (k.E)=mv2 K.E (He)2mHe"He) (5) 2 Th'Th mHe K.E(He m 2" Не Th 2 Th Th (Не Th -Κ.Ε (Th (Не K.Е(Не) 234.043594 (6) 4.002603 Κ.Ε (Th) fullscreen

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