Year 11 / Ionising radiation and nuclear reactions

A small mass difference matters.

The mass of a bound nucleus is less than the total mass of its separated nucleons. The difference corresponds to binding energy. In a reaction, a lower total final rest mass means energy has been released into kinetic energy and radiation.

Fission splits a heavy nucleus and can release neutrons that sustain a chain reaction. Fusion joins light nuclei; high temperatures help nuclei overcome electrostatic repulsion. Both can release energy when the products have greater binding energy per nucleon.

INTERACTIVE MODEL

Rest mass becomes energy

Number of identical reactions1

READ THE GRAPH

Explore the relationship

E = Δmc² with c = 3.00 × 10⁸ m s⁻¹.

Released energy / 10⁻¹³ J

Tap or focus a plotted point to read its values.

View plotted data as a table

Explore the relationship
Series	Mass defect per reaction / 10⁻²⁹ kg	Released energy / 10⁻¹³ J
Released energy / 10⁻¹³ J	0	0
Released energy / 10⁻¹³ J	0.166667	1.5
Released energy / 10⁻¹³ J	0.333333	3
Released energy / 10⁻¹³ J	0.5	4.5
Released energy / 10⁻¹³ J	0.666667	6
Released energy / 10⁻¹³ J	0.833333	7.5
Released energy / 10⁻¹³ J	1	9
Released energy / 10⁻¹³ J	1.16667	10.5
Released energy / 10⁻¹³ J	1.33333	12
Released energy / 10⁻¹³ J	1.5	13.5
Released energy / 10⁻¹³ J	1.66667	15
Released energy / 10⁻¹³ J	1.83333	16.5
Released energy / 10⁻¹³ J	2	18
Released energy / 10⁻¹³ J	2.16667	19.5
Released energy / 10⁻¹³ J	2.33333	21
Released energy / 10⁻¹³ J	2.5	22.5
Released energy / 10⁻¹³ J	2.66667	24
Released energy / 10⁻¹³ J	2.83333	25.5
Released energy / 10⁻¹³ J	3	27
Released energy / 10⁻¹³ J	3.16667	28.5
Released energy / 10⁻¹³ J	3.33333	30
Released energy / 10⁻¹³ J	3.5	31.5
Released energy / 10⁻¹³ J	3.66667	33
Released energy / 10⁻¹³ J	3.83333	34.5
Released energy / 10⁻¹³ J	4	36
Released energy / 10⁻¹³ J	4.16667	37.5
Released energy / 10⁻¹³ J	4.33333	39
Released energy / 10⁻¹³ J	4.5	40.5
Released energy / 10⁻¹³ J	4.66667	42
Released energy / 10⁻¹³ J	4.83333	43.5
Released energy / 10⁻¹³ J	5	45
Released energy / 10⁻¹³ J	5.16667	46.5
Released energy / 10⁻¹³ J	5.33333	48
Released energy / 10⁻¹³ J	5.5	49.5
Released energy / 10⁻¹³ J	5.66667	51
Released energy / 10⁻¹³ J	5.83333	52.5
Released energy / 10⁻¹³ J	6	54
Released energy / 10⁻¹³ J	6.16667	55.5
Released energy / 10⁻¹³ J	6.33333	57
Released energy / 10⁻¹³ J	6.5	58.5
Released energy / 10⁻¹³ J	6.66667	60
Released energy / 10⁻¹³ J	6.83333	61.5
Released energy / 10⁻¹³ J	7	63
Released energy / 10⁻¹³ J	7.16667	64.5
Released energy / 10⁻¹³ J	7.33333	66
Released energy / 10⁻¹³ J	7.5	67.5
Released energy / 10⁻¹³ J	7.66667	69
Released energy / 10⁻¹³ J	7.83333	70.5
Released energy / 10⁻¹³ J	8	72
Released energy / 10⁻¹³ J	8.16667	73.5
Released energy / 10⁻¹³ J	8.33333	75
Released energy / 10⁻¹³ J	8.5	76.5
Released energy / 10⁻¹³ J	8.66667	78
Released energy / 10⁻¹³ J	8.83333	79.5
Released energy / 10⁻¹³ J	9	81
Released energy / 10⁻¹³ J	9.16667	82.5
Released energy / 10⁻¹³ J	9.33333	84
Released energy / 10⁻¹³ J	9.5	85.5
Released energy / 10⁻¹³ J	9.66667	87
Released energy / 10⁻¹³ J	9.83333	88.5
Released energy / 10⁻¹³ J	10	90

Probe along the horizontal axis0Released energy / 10⁻¹³ J: 0

Explore: Change the mass defect and see how energy release scales.

E=\Delta m c^2

WORKED EXAMPLE

A reaction loses 2.0 × $10^{-29}$ kg of rest mass. Use c = 3.0 × $10^{8}$ $\mathrm{m}\,\mathrm{s}^{-1}$ .

E = 2.0 × $10^{-29}$ × (3.0 × $10^{8}$ )².
E = 1.8 × $10^{-12}$ J.

Assumed knowledge

Scientific notation and squaring.

Learning checkpoints & source

YOUR LEARNING CHECKPOINT

Relate mass defect to energy release.
Compare fission, fusion and chain reactions.

QCAA Physics · Unit 1 · Ionising radiation and nuclear reactions ↗

READY TO TRY IT?

A small mass difference matters.

Rest mass becomes energy

Explore the relationship

A reaction loses 2.0 × 10−2910^{-29}10−29 kg of rest mass. Use c = 3.0 × 10810^{8}108 m s−1\mathrm{m}\,\mathrm{s}^{-1}ms−1.

Put the idea to work.

A reaction loses 2.0 × $10^{-29}$ kg of rest mass. Use c = 3.0 × $10^{8}$ $\mathrm{m}\,\mathrm{s}^{-1}$ .