PhysicsICSE Class 10 · Radioactivity

Alpha and Beta Decay: Nuclear Equations and Changes in Z and A (ICSE Class 10)

Updated 16 October 2026 · Fact-checked

In alpha decay a nucleus emits a helium nucleus, so its mass number A falls by 4 and atomic number Z by 2; the new element is two places to the left in the periodic table. In beta decay a neutron becomes a proton and an emitted electron, so A is unchanged and Z rises by 1.

In alpha decay A falls by 4 and Z by 2; in beta decay a neutron (ringed) becomes a proton, so A stays the same and Z rises by 1.

Illustration drawn for QuestionBuddy.

Understand Alpha and Beta Decay

The nucleus (qualitative). At the centre of an atom is a tiny, dense nucleus made of protons (charge $+ e$ ) and neutrons (no charge), together called nucleons.

Atomic number $Z$ : the number of protons. It decides which element the atom is.
Mass number $A$ : the number of nucleons (protons + neutrons).
Number of neutrons: $N = A - Z$ .

A nucleus of element X is written $_{Z}^{A} X$ . Isotopes have the same $Z$ but different $A$ (different numbers of neutrons); isobars have the same $A$ but different $Z$ .

Radioactive decay. Some nuclei are unstable. They spontaneously emit radiation and change into other nuclei. The three radiations are α (alpha), β (beta) and γ (gamma).

Alpha decay. An α particle is a helium nucleus, $_{2}^{4} He$ (2 protons and 2 neutrons). The nucleus loses these, so:

$_{Z}^{A} X \to_{Z - 2}^{A - 4} Y +_{2}^{4} He$

$A$ decreases by 4, $Z$ by 2, $N$ by 2.
The daughter is a new element, two places to the left in the periodic table.
Example: $_{95}^{241} Am \to_{93}^{237} Np +_{2}^{4} He$ .

Beta decay. Inside the nucleus, a neutron changes into a proton and an electron; the electron is shot out as the β particle, $_{- 1}^{0} e$ :

$_{0}^{1} n \to_{1}^{1} p +_{- 1}^{0} e$

$_{Z}^{A} X \to_{Z + 1}^{A} Y +_{- 1}^{0} e$

$A$ (the number of nucleons) is unchanged: one neutron has simply become a proton.
$Z$ increases by 1; $N$ decreases by 1.
The daughter is one place to the right in the periodic table.
Example: $_{15}^{32} P \to_{16}^{32} S +_{- 1}^{0} e$ .

The nucleus contains no electrons; the β electron is created at the moment of decay.

Gamma emission. After α or β decay the new nucleus is often left with extra energy, which it gives out as a γ ray. **Neither $A$ nor $Z$ changes**: $_{Z}^{A} X^{*} \to_{Z}^{A} X + γ$ .

Balancing nuclear equations. In every equation, the **sum of the top numbers ( $A$ ) and the sum of the bottom numbers ( $Z$ )** are the same on both sides.

Summary table.

Emission	Change in A	Change in Z	Change in N	Periodic table
α	−4	−2	−2	2 places left
β	0	+1	−1	1 place right
γ	0	0	0	No change

Decay chains. A nucleus often decays in several steps. Work one step at a time, writing each daughter before the next emission. Useful results:

One α followed by two β: $A$ falls by 4, $Z$ returns to its original value, so the final nucleus is an isotope of the original (with 4 fewer neutrons).
To count emissions from $_{Z_{1}}^{A_{1}} X$ to $_{Z_{2}}^{A_{2}} Y$ : only α changes $A$ , so $n_{α} = \frac{A _{1} - A _{2}}{4}$ ; then $n_{β} = 2 n_{α} - (Z_{1} - Z_{2})$ .

Alpha and Beta Decay: formulas and key facts

Neutron number: $N = A - Z$; A = protons + neutrons.
Alpha decay: $_{Z}^{A} X \to_{Z - 2}^{A - 4} Y +_{2}^{4} He$; Two places left.
Beta decay: $_{Z}^{A} X \to_{Z + 1}^{A} Y +_{- 1}^{0} e$; A neutron becomes a proton; one place right.
Counting α and β: $n_{α} = \frac{A _{1} - A _{2}}{4}, n_{β} = 2 n_{α} - (Z_{1} - Z_{2})$; Only α changes A.

How to solve Alpha and Beta Decay questions

Treat each emission as a separate step and keep two running totals: A on top, Z below.

1Write the parent as $_{Z}^{A} X$ and find $N = A - Z$ if needed.
2For α: subtract 4 from A and 2 from Z. For β: keep A, add 1 to Z. For γ: no change.
3In a chain, write each daughter in full before applying the next emission; emitted particles are not reactants for the next step.
4To work backwards, reverse each step: undo β by subtracting 1 from Z; undo α by adding 4 to A and 2 to Z.
5Check by balancing: top numbers and bottom numbers must add up the same on both sides.
6For periodic-table questions, use the net change in Z: −2 is two places left, +1 is one place right.

Alpha and Beta Decay in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

The source inside a smoke detector

Suppose you open the cover of a household ionisation smoke detector and find a label: 'Contains americium-241'. Americium-241 (Z = 95) is an α emitter.

Write the decay equation and name the daughter element (Z = 93 is neptunium).

Try it first, then show the solutionSolution

α decay: A falls by 4 and Z by 2.
$_{95}^{241} Am \to_{93}^{237} Np +_{2}^{4} He$ .

Answer: Neptunium-237 is formed; it lies two places to the left of americium.

Memory hook: Alpha: minus 4 on top, minus 2 below.

Radon in the soil

Imagine your science teacher says that radon-222 (Z = 86), a radioactive gas that seeps out of some rocks, decays by α emission to polonium (Z = 84).

Find the mass number of the polonium formed and its number of neutrons.

Try it first, then show the solutionSolution

α decay: $A = 222 - 4 = 218$ , $Z = 86 - 2 = 84$ .
$N = 218 - 84 = 134$ .

Answer: Polonium-218, with 134 neutrons.

Memory hook: Work top and bottom separately.

Tricks to remember Alpha and Beta Decay

Short memory aids. Say each one aloud once, then use it on a question the same day.

Alpha is heavy: 4 and 2
α carries away a whole helium nucleus: A − 4, Z − 2 ('Alpha leaves two steps back').
Use it when: Alpha decay changes.
Beta: same weight, one more charge
Neutron → proton + electron: A same, Z + 1 ('Beta steps one forward').
Use it when: Beta decay changes.
One alpha, two betas: back home
After α + 2β, Z is back to start: an isotope with 4 fewer nucleons.
Use it when: Chain questions.
Top and bottom must balance
Add the top numbers on each side; add the bottom numbers on each side.
Use it when: Checking nuclear equations.

Alpha and Beta Decay: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: After a β emission · 1 mark · MCQBoard level

A nucleus $_{Z}^{A} X$ emits one β particle. The new nucleus is:
(a) $_{Z - 1}^{A} Y$
(b) $_{Z + 1}^{A} Y$
(c) $_{Z}^{A - 1} Y$
(d) $_{Z - 2}^{A - 4} Y$

Try it first, then show the solutionSolution

A neutron becomes a proton: A unchanged, Z increases by 1.

Answer: (b) $_{Z + 1}^{A} Y$

Example 2: Americium's α decay · 3 marks · Short answerBoard level

For $_{95}^{241} Am$ : (a) state the number of protons and neutrons; (b) write the equation for its α decay, naming the daughter as Np; (c) where is Np in the periodic table relative to Am?

Try it first, then show the solutionSolution

(a) Protons $= 95$ ; neutrons $= 241 - 95 = 146$ . (1)
(b) $_{95}^{241} Am \to_{93}^{237} Np +_{2}^{4} He$ . (1)
(c) Two places to the left (Z falls by 2). (1)

Answer: (a) 95 and 146 (b) ²⁴¹₉₅Am → ²³⁷₉₃Np + ⁴₂He (c) Two places left

Example 3: Inside a β decay · 3 marks · Short answerHarder board level

Phosphorus-32, $_{15}^{32} P$ , is a β emitter. (a) Write the decay equation, naming the product as S. (b) What change takes place inside the nucleus? (c) Find the number of neutrons before and after.

Try it first, then show the solutionSolution

(a) $_{15}^{32} P \to_{16}^{32} S +_{- 1}^{0} e$ . (1)
(b) A neutron changes into a proton and an electron; the electron is emitted as the β particle. (1)
(c) Before: $32 - 15 = 17$ ; after: $32 - 16 = 16$ . (1)

Answer: (a) ³²₁₅P → ³²₁₆S + ⁰₋₁e (b) n → p + e (c) 17 and 16

Example 4: A three-step chain · 3 marks · Short answerHarder board level

$_{84}^{218} X$ emits an α particle to form Y. Y emits a β particle to form Z, and Z emits a β particle to form W. (a) Find A and Z for Y, Z and W. (b) How are X and W related?

Try it first, then show the solutionSolution

(a) Y: $_{82}^{214}$ ; Z: $_{83}^{214}$ ; W: $_{84}^{214}$ . (2)
(b) Same atomic number (84), different mass number: W is an isotope of X. (1)

Answer: (a) Y ²¹⁴₈₂, Z ²¹⁴₈₃, W ²¹⁴₈₄ (b) Isotopes

Example 5: Working backwards · 2 marks · Short answerHarder board level

A nucleus emits one α particle and then one β particle, ending as $_{82}^{206} Pb$ . Find the mass number and atomic number of the original nucleus.

Try it first, then show the solutionSolution

Undo the β: before it, A = 206 and Z = 82 − 1 = 81. (1)
Undo the α: A = 206 + 4 = 210, Z = 81 + 2 = 83. Original: $_{83}^{210}$ . (1)

Answer: A = 210, Z = 83

Example 6: Counting the emissions · 3 marks · Short answerHOTS / competency

$_{92}^{235} U$ decays through a series of α and β emissions to stable $_{82}^{207} Pb$ . Find the numbers of α and β particles emitted.

Try it first, then show the solutionSolution

Only α changes A: $n_{α} = \frac{235 - 207}{4} = 7$ . (1)
Seven α would lower Z by 14, to 78. (1)
Z must rise from 78 to 82, so $n_{β} = 4$ . (1)

Answer: 7 α and 4 β

Example 7: Case study: a neutron–proton graph · 4 marks · Case-basedHOTS / competency

On a graph of number of neutrons (y-axis) against number of protons (x-axis), nucleus P is at (92, 146).
(a) Find the mass number of P.
(b) P emits an α particle to form Q. Give the coordinates of Q.
(c) Q emits a β particle to form R. Give the coordinates of R.
(d) R emits a further β particle to form S. Compare S with P.

Try it first, then show the solutionSolution

(a) $A = 92 + 146 = 238$ . (1)
(b) α: 2 protons and 2 neutrons lost: Q at (90, 144). (1)
(c) β: one neutron becomes a proton: R at (91, 143). (1)
(d) S at (92, 142): same protons as P (an isotope), 4 fewer neutrons, mass number 234. (1)

Answer: (a) 238 (b) (90, 144) (c) (91, 143) (d) Isotope of P with 4 fewer neutrons (A = 234)

Where students lose marks in Alpha and Beta Decay

The slips examiners see most often, and what to write instead.

Mistake: Changing the nucleon number in β decay
A neutron becomes a proton, so the total number of nucleons stays the same.
Wrong working
'Z goes up by 1, so the number of nucleons goes up by 1.'
Right working
'A is unchanged; Z increases by 1.'
Do this: Write n → p + e and count nucleons before and after.
Usually costs: Reported by CISCE examiners for 2024 Q1(iv).
Mistake: Chained equations done in one go
Sequential emissions must be handled step by step; the emitted particles are not reactants for the next step.
Wrong working
Trying to undo an α and a β emission together and getting the wrong parent.
Right working
Write each daughter separately, then reverse one step at a time.
Do this: Split the chain into separate equations.
Usually costs: Reported by CISCE examiners for 2024 Q7(ii).
Mistake: Wrong side of the periodic table
α lowers Z by 2, so the new element is two places to the left.
Wrong working
'After α emission, the element moves two groups to the right.'
Right working
'Two places to the left (Z − 2).'
Do this: Lower Z = further left.
Usually costs: Reported by CISCE examiners for 2025 Q1(xiii).
Mistake: Misreading a neutron–proton graph
The axes show numbers of protons and neutrons, not Z and A.
Wrong working
Treating the neutron axis as mass number and applying only the Z change for α.
Right working
α: protons − 2, neutrons − 2; β: protons + 1, neutrons − 1.
Do this: Read the axis labels and convert A to N = A − Z first.
Usually costs: Reported by CISCE examiners for 2025 Q3(vii).

Exam tips

Write every nuclear symbol with both A (top) and Z (bottom).
Show that A and Z balance on both sides of each equation.
In a chain, give the intermediate nuclei even if only the last is asked.
Give the β particle as $_{- 1}^{0} e$ and the α particle as $_{2}^{4} He$ .

Practice questions on Alpha and Beta Decay

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
In β decay, which change takes place inside the nucleus?
(a) a proton becomes a neutron
(b) a neutron becomes a proton
(c) two protons and two neutrons leave
(d) an electron orbiting the nucleus is captured
Hint
Z increases.
Answer
(b) a neutron becomes a proton
Q2 · 1 mark · Very short answerBoard level
Find the number of neutrons in $_{19}^{40} K$ .
Hint
$N = A - Z$ .
Answer
$40 - 19 = 21$ .
Q3 · 1 mark · Very short answerBoard level
Complete: $_{27}^{60} Co \to_{?}^{60} Ni +_{- 1}^{0} e$ . Name the decay.
Hint
Balance the bottom numbers.
Answer
28; β decay.
Q4 · 2 marks · Short answerHarder board level
Write the equation for the α decay of $_{94}^{239} Pu$ , naming the product as U.
Hint
A − 4, Z − 2.
Answer
$_{94}^{239} Pu \to_{92}^{235} U +_{2}^{4} He$ .
Q5 · 2 marks · Short answerHarder board level
A nucleus emits two α particles and one β particle. By how much do its mass number and atomic number change?
Hint
Add the changes.
Answer
A falls by $2 \times 4 = 8$ ; Z changes by $2 \times (- 2) + 1 = - 3$ (falls by 3).
Q6 · 2 marks · Short answerHarder board level
$_{83}^{212} X$ emits a β particle to form Y, and Y emits an α particle to form Z. Find A and Z of Y and Z.
Hint
One step at a time.
Answer
Y: $_{84}^{212}$ ; Z: $_{82}^{208}$ .
Q7 · 2 marks · Short answerHarder board level
Why does the mass number of a nucleus not change when it emits a β particle?
Hint
What happens to the neutron?
Answer
A neutron changes into a proton (and an electron, which is emitted). The number of nucleons stays the same, so A is unchanged; only Z increases by 1.
Q8 · 2 marks · Short answerHarder board level
From $_{18}^{40} Ar$ , $_{19}^{40} K$ and $_{19}^{39} K$ , name a pair of isotopes and a pair of isobars.
Hint
Same Z or same A.
Answer
Isotopes: $_{19}^{39} K$ and $_{19}^{40} K$ (same Z). Isobars: $_{18}^{40} Ar$ and $_{19}^{40} K$ (same A).
Q9 · 3 marks · Short answerHOTS / competency
$_{88}^{226} Ra$ decays through α and β emissions to $_{82}^{206} Pb$ . Find the number of each.
Hint
Use A first.
Answer
$n_{α} = \frac{226 - 206}{4} = 5$ ; five α lower Z to 78; to reach 82, $n_{β} = 4$ .
Q10 · 2 marks · Short answerHOTS / competency
A nucleus contains no electrons, yet it can emit a β particle, which is an electron. Explain.
Hint
Where does the electron come from?
Answer
The electron is created at the moment of decay, when a neutron in the nucleus changes into a proton and an electron. The proton stays in the nucleus and the electron is emitted.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Change in A and Z in α decay?Show answer
A − 4, Z − 2.
2.Change in A and Z in β decay?Show answer
A unchanged, Z + 1.
3.Change in A and Z in γ emission?Show answer
None.
4.What does a neutron change into in β decay?Show answer
A proton and an electron.
5.Result of one α and two β emissions?Show answer
An isotope of the original (A − 4).

Alpha and Beta Decay: frequently asked questions

What happens in alpha decay?

The nucleus emits an α particle (a helium nucleus, ⁴₂He). Its mass number falls by 4 and its atomic number by 2, so it becomes a new element two places to the left in the periodic table.

What happens in beta decay?

A neutron in the nucleus changes into a proton and an electron, and the electron is emitted as the β particle. The mass number is unchanged and the atomic number increases by 1.

How do you find the number of α and β particles emitted in a decay series?

Only α changes the mass number, so nα = (A₁ − A₂)/4. Then find how much the α emissions alone would lower Z; the number of β emissions is what is needed to bring Z up to the final value.