13.17 The fission properties of are very similar to those of . The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure undergo fission?
13.17 The average energy released per fission of = 180 MeV
Amount of pure , m = 1 kg = 1000 g
Avogadro's number, = 6.023
Mass number of = 239 gm
Hence, number of atoms in 1000 g , N =
= 2.52
Total energy released during the fission of 1 kg of , E =
N
= 180 2.52 MeV = 4.536 MeV
<p><strong>13.17 </strong>The average energy released per fission of <span title="Click to copy mathml"><math><mmultiscripts><mrow><mrow><mi>P</mi><mi>u</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>94</mn></mrow></mrow><mrow><mrow><mn>239</mn></mrow></mrow></mmultiscripts></math></span> <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>E</mi></mrow></mrow><mrow><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></mrow></msub></math></span>= 180 MeV</p><p>Amount of pure<span title="Click to copy mathml"><math><mmultiscripts><mrow><mrow><mi>u</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>94</mn></mrow></mrow><mrow><mrow><mn>239</mn></mrow></mrow></mmultiscripts></math></span> , m = 1 kg = 1000 g</p><p>Avogadro's number, <span title="Click to copy mathml"><br></span><span title="Click to copy mathml"><math><msub><mrow><mrow><mi>N</mi></mrow></mrow><mrow><mrow><mi>A</mi></mrow></mrow></msub></math></span> = 6.023 <span title="Click to copy mathml"><math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>23</mn></mrow></mrow></msup></math></span></p><p>Mass number of <span contenteditable="false"> <math> <mmultiscripts> <mrow> <mrow> <mi mathvariant="bold-italic">P</mi> <mi mathvariant="bold-italic">u</mi> </mrow> </mrow> <mprescripts></mprescripts> <mrow> <mrow> <mn>94</mn> </mrow> </mrow> <mrow> <mrow> <mn>239</mn> </mrow> </mrow> </mmultiscripts> </math> </span> = 239 gm</p><p>Hence, number of atoms in 1000 g <span title="Click to copy mathml"><math><mmultiscripts><mrow><mrow><mi>P</mi><mi>u</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>94</mn></mrow></mrow><mrow><mrow><mn>239</mn></mrow></mrow></mmultiscripts></math></span>, N =<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>6.023</mn><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>23</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>239</mn></mrow></mrow></mfrac></math></span> <span title="Click to copy mathml"><math><mo>*</mo><mn>1000</mn></math></span>= 2.52 <span title="Click to copy mathml"><math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>24</mn></mrow></mrow></msup></math></span></p><p>Total energy released during the fission of 1 kg of <span title="Click to copy mathml"><math><mmultiscripts><mrow><mrow><mi>P</mi><mi>u</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>94</mn></mrow></mrow><mrow><mrow><mn>239</mn></mrow></mrow></mmultiscripts></math></span>, E =<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>E</mi></mrow></mrow><mrow><mrow><mi>a</mi><mi>v</mi><mi>g</mi></mrow></mrow></msub></math></span> <span title="Click to copy mathml"><math><mo>*</mo></math></span>N</p><p>= 180 <span title="Click to copy mathml"><math><mo>*</mo></math></span> 2.52<span title="Click to copy mathml"><math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>24</mn></mrow></mrow></msup></math></span> MeV = 4.536 <span title="Click to copy mathml"><math><mo>*</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>26</mn></mrow></mrow></msup></math></span> MeV</p>
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