Nucleus Mass (u) 1.00783 4He 4.00260 8Be 8.00530 12c 12.00000 Listed above are t

Question

Nucleus Mass (u) 1.00783 4He 4.00260 8Be 8.00530 12c 12.00000 Listed above are the masses of four different nuclei (1 u = 1.6606 x 10-27 kg). (a) Based on energy considerations, which of the four reactions listed below can actually produce energy? Mark ALL that are possible. 41H 4He 3 4He+ 12C (b) The first reaction actually occurs in some stars. What is the amount of energy produced per reaction for this process? 4.28 PJ (c) suppose we could produce energy this way, with 100% efficiency. How many kg of hydrogen would be required to power a 2.30 GW power plant for one day? Enter a number differs from the correct answer by more than 10%. Double check your calculations. kg

Explanation / Answer

given

mass of 1H = 1.00783

mass of 4He = 4.00260

mass of 8 Be = 8.00530

mass of 12 C = 12

a) if mass of products is less than mass of reactants then the reaction can take place

for 4 1H -> 4He , dm < 0 hence reaction is possible

for 2 4He -> 8Be , dm > 0 hence reaction not possible

for 4He + 8Be -> 12 C, dm < 0 hence reaction is possible

for 3 4He -> 12 C, dm < 0 HENCE THE reaction is possible

b) for first reaction dm = -0.02872

SO energy produced per reaction = -dm*c^2 *1.66*10^-27= 4.290768*10^-12 J

c) for 2.3 GW Power, P = 2.3*10^9 W

in one day, energy utilisation = P*24*60*60 J

so number of reactions required , n = P*24*60*60/4.290768*10^-12 = 4.631*10^25 reactions

number of H atoms required = 4n

number of moles of H atoms required = 4n/A [ where A = 6.022*10^23 , avogadros number]

Hence, 307.627 mole of H atoms are requires

1 mole H atoms weigth 1.00783 grams

so mass of hydrogen required = 310.03667 grams = 0.310 kg

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