1st one: In a nuclear fusion reaction two 2H atoms are combined to produce 4He. Taking M(2H) = 2.014102 u and M(4He) = 4.002602 u, how much energy in MeV is released in this reaction?
2nd one: In a nuclear fusion reaction two 2H atoms are combined to produce 4He. Taking M(2H) = 2.014102 u and M(4He) = 4.002602 u, how many such reactions must take place per second to produce 92 watt of power?
Any Help is appreciated!
2 Answers
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1. The mass deficit of this reaction is 2*2.014102 – 4.002602 = 0.025602 u
The energy released from this reaction is the conversion of the mass deficit into energy from Einstein’s mass-energy relationship,
The energy released is mass deficit times 931.5 Mev/u
so E = 0.025602u*931.5Mev/u = 23.848MeV
2. This energy corresponds to 23.848MeV*1.60×10^-13J/Mev = 3.8157×10^-12J
so to produce 92J/s we would need 92/3.8157×10^-12 = 2.411×10^13 reactions per second
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Einstein’s mass-energy equivalence,,
E=mC^2
where C is the velocity of light i.e 3*10^ 8m/s.
The mass of 2H converts into energy so,
E= (2.014102) * ( 3*10^8)^2
E= (2.014102) * 9 * 10^16
E= 1.81269*10^17 electron volts
and 1.81269*10^17 electron volts is equal to 4.8*10^-19 joules.
E= 4.8*10^-19 joules.
As
Power = Energy / time
How many reactions must take place per 1 second to produce 92 watt of power. For this put values
92 = Energy / 1 second.
92*1=Energy
Energy = 92 joules. ..( 92 joules of energy is required for 92 watt power and how many reactions..?)
1 reaction produce Energy of 4.8*10^-19 joules.
1 reaction= 4.8*10^-19 joules
And how many reactions produce 92 joules of energy For this,.
X reactions = 92 joules
Divide both sides by 1 reaction.
X reactions / 1 reaction = 92 / 1 reaction
X reactions = 92 / 4.8*10^-19 …..( as 1 reaction = 4.8*10^-19)
X reactions = 1.9*10^20
hence 1.9*10^20 reactions must take place to produce 92 watt of power.
