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6 May, 18:14

Be sure to answer all parts. Plutonium-242 decays to uranium-238 by emission of an α particle with an energy of 4.853 MeV. The 238U that forms is unstable and emits a γ ray (λ = 0.02757 nm). (a) Write a balanced net equation for these reactions. → (b) What would be the energy of the α particle if 242Pu decayed directly to the more stable 238U? MeV

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  1. 6 May, 18:33
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    (a) ²⁴²₉₄Pu ⇒ ⁴₂He + ²³⁸₉₂U ⇒ ²³⁸₉₂U + ⁰₀γ

    (b) 4.898 MeV

    Explanation:

    In the nuclear reaction, it was stated that plutonium-242 decayed firstly to uranium-238 and alpha, and lastly to a stable uranium-238 by emitting a gamma ray. The balanced equation for the nuclear reactions is shown below:

    (a) ²⁴²₉₄Pu ⇒ ⁴₂He + ²³⁸₉₂U ⇒ ²³⁸₉₂U + ⁰₀γ

    (b) The energy emitted by releasing a gamma ray is calculated using:

    E = hc/λ

    where

    h = 4.136*10^-15 eV. s

    c = 299792458 m/s

    λ = 0.02757 nm = 0.02757*10^-9 m

    Therefore:

    E = (4.136*10^-15) * (299792458) / 0.02757*10^-9 = 44974.31 eV

    The total energy if the stable 238U was produced directly would be

    4.853*10^6 + 44974.31 = 4.898 MeV
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