Question

Calculate the energy released (in gigajoules) when 2.139 g uranium undergoes the following reaction: ¹₀n + ²³⁵₉₂U --> ¹³⁶₅₃I + ⁹⁶₃₉Y + 4¹₀n if the mass of U-235 is 234.9935 amu, I-136 is 135.8401 amu and Y-96 95.8629 amu. (Hints: 1 gigajoule = 1x10⁹ joules; enter your answer as a positive number with no decimal places.)

Answer 1

¹₀n + ²³⁵₉₂U --> ¹³⁶₅₃I + ⁹⁶₃₉Y + 4¹₀n

first we find mass defect  Δm

Δm = calculated mass - observed mass

mass of reactant side = (¹₀n = 1.008665 amu + and ²³⁵₉₂U = 234.9935 amu ) = 236.002165 amu

mass of product side = (¹³⁶₅₃I = 135.8401 amu + ⁹⁶₃₉Y = 95.8629 amu + 4¹₀n = 4.03466 amu ) = 235.73766 amu

Δm = 236.002165 amu - 235.73766 amu = 0.264505 amu

ΔE = Δm.c²

ΔE = (0.264505 amu x 3.00 x10⁸ )² m/s

{ 1 amu = 1.66x10^-27 kg so, 0.264505 amu = 4.390783 x10^-28 kg }  

ΔE = {4.390783 x10^-28kg x (3.00 x10⁸ )² m/s }

ΔE = 3.952x10^-11 J for 1 atom

now find moles of uranium = ( mass / molar weight) = (2.139 g / 235.044 g/mol) = 0.0091 moles

ΔE = 3.952x10^-11 J x (6.022x10²³ x 0.0091 moles ) = 2.1658x10¹¹ J

ΔE = 216.58 gigajoules ~ 217 gigajoules