(a) Calculate in MeV the energy released in the fission reaction 235 U + In 140Xe + ⁹4Sr + 2n The atomic masses are 235.04392 u, 139.92144 u and 93.91523 u, respectively. Take the mass of a neutron as 1.00866 u. (b) Using energy considerations, the power P required to propel a submerged submarine may be estimated from its diameter D and speed V according to (i) (ii) 1 AD² ==p² (iii) Show by dimensional analysis that the right-hand side of the equation has the dimensions of power. Estimate the power in MW required to propel a 10 m diameter submarine at 30 km/h. The density of water is approximately 1000 kg/m³. Using your result from (a), estimate how many U-235 fissions per second are required to achieve such a power. (Avogadro's constant is 6.022 ×1023 mol-¹.)

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(a) Calculate in MeV the energy released in the fission reaction
235 U + In
40 Xe + ⁹4Sr + 2n
The atomic masses are 235.04392 u, 139.92144 u and 93.91523 u, respectively. Take the
mass of a neutron as 1.00866 u.
(b) Using energy considerations, the power P required to propel a submerged submarine may
be estimated from its diameter D and speed V according to
(i)
(ii)
1 AD²
=p²
(iii)
Show by dimensional analysis that the right-hand side of the equation has the dimensions
of power.
Estimate the power in MW required to propel a 10 m diameter submarine at 30 km/h. The
density of water is approximately 1000 kg/m³.
Using your result from (a), estimate how many U-235 fissions per second are required to
achieve such a power.
(Avogadro's constant is 6.022 ×1023 mol-¹.)
Transcribed Image Text:(a) Calculate in MeV the energy released in the fission reaction 235 U + In 40 Xe + ⁹4Sr + 2n The atomic masses are 235.04392 u, 139.92144 u and 93.91523 u, respectively. Take the mass of a neutron as 1.00866 u. (b) Using energy considerations, the power P required to propel a submerged submarine may be estimated from its diameter D and speed V according to (i) (ii) 1 AD² =p² (iii) Show by dimensional analysis that the right-hand side of the equation has the dimensions of power. Estimate the power in MW required to propel a 10 m diameter submarine at 30 km/h. The density of water is approximately 1000 kg/m³. Using your result from (a), estimate how many U-235 fissions per second are required to achieve such a power. (Avogadro's constant is 6.022 ×1023 mol-¹.)
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