Fenella is handed a nuclear reaction's full accounts: the mass of everything going in, and the mass of everything coming out. Two numbers. From them, she can say exactly how much energy the reaction released, and where it went.
You have the three tools already. Mass sits on the conservation ledger. An energy-releasing nuclear reaction's products end up with slightly less total mass: the mass defect. And you can convert a mass into its energy equivalent, with the equation and the value of c always given. This lesson chains the three into one routine.
A nuclear reaction's books are two numbers: the total mass before, and the total mass after.
Suppose the reactants total 5.030 × 10⁻²⁷ kg and the products total 5.000 × 10⁻²⁷ kg.
Step one: subtract to find the mass defect, the before total minus the after total.
Step two: convert the defect with E = mc², the equation and the value of c given.
Step three: state where the released energy ends up on the conservation ledger.
Reactants total 5.030 × 10⁻²⁷ kg; products total 5.000 × 10⁻²⁷ kg. Find the energy released and state where it goes. Use E = mc², with c = 3.00 × 10⁸ m/s.
Write down the values: before, 5.030 × 10⁻²⁷ kg; after, 5.000 × 10⁻²⁷ kg.
Subtract: 5.030 minus 5.000 is 0.030, so the mass defect is 0.030 × 10⁻²⁷ kg, which is 3.0 × 10⁻²⁹ kg.
Square c: c² is 9.00 × 10¹⁶ J/kg.
Convert: 3.0 × 9.00 = 27, and the powers of ten make 10⁻¹³. So E = 27 × 10⁻¹³ J.
E = 2.7 × 10⁻¹² J, carried off by the fragments and radiation. The ledger balances.
In a fusion reaction inside a tokamak, the products end up lighter than the reactants. State where the released energy ends up on the ledger.
The missing mass converted to released energy.
The products carry that energy away: the new nucleus and the released particles fly apart at enormous speed.
The released energy leaves as the products' kinetic energy, and the ledger balances.
In one nuclear reaction, the reactants total 8.070 × 10⁻²⁷ kg and the products total 8.030 × 10⁻²⁷ kg. Calculate the mass defect, in kilograms, to two significant figures.
A fusion event's mass defect is 6.0 × 10⁻²⁹ kg. Use E = mc², with c = 3.00 × 10⁸ m/s, to calculate the energy released, in joules, to two significant figures.
A nuclear reaction's products total slightly less mass than its reactants. On the conservation ledger, what balances the missing mass?
A nuclear reaction's reactants total 3.360 × 10⁻²⁷ kg and its products total 3.340 × 10⁻²⁷ kg. Use E = mc², with c = 3.00 × 10⁸ m/s, to calculate the energy released, in joules, to two significant figures.
In one fission event, the nucleus plus its absorbed neutron total 3.920 × 10⁻²⁵ kg before the split, and the fragments plus released neutrons total 3.915 × 10⁻²⁵ kg after. Use E = mc², with c = 3.00 × 10⁸ m/s, to calculate the energy released, in joules, to two significant figures.
Which line correctly closes the mass-energy books on an energy-releasing nuclear reaction?