GCSE · Physics · Edexcel · Spec 1PH0

Balancing nuclear equations

Some nuclei throw out a particle and turn into a different element. You can predict exactly what is left with just two sums: top numbers and bottom numbers.

Physics · Radioactive decay

One nucleus, three ways to decay

Choose what the nucleus emits. Read what happens to the mass number (top) and the atomic number (bottom), then check the totals.

What is emitted

3 decay routes.

On Parent nucleus: mass number A, atomic number Z. 3 branches to choose from.

Pick what the nucleus emits and see what is left behind.

Exam line: Whatever is emitted, daughter + emitted particle must add up to the parent on the top row and on the bottom row.

Watch out: These are three different routes. A nucleus takes one of them each time it decays; they are not stages of one process.

Worked example: alpha decay with a missing daughter

Problem

Radium-226 (²²⁶₈₈Ra) decays by alpha emission. Write the balanced nuclear equation and name the daughter.

Physics · Your turn

Beta-minus: you supply the missing steps

Strontium-90 (⁹⁰₃₈Sr) decays by beta-minus emission. Find the daughter nucleus.

Write the equation with an unknown daughter: ⁹⁰₃₈Sr → (A, Z)X + ⁰₋₁eCall the daughter's mass number A and its atomic number Z.
missing step

Which line is step 2?

Top row: 90 = A + 0, so A = 90Top row: 90 = A + 4, so A = 86Top row: 90 = A − 1, so A = 91

Exam line: Put the beta-minus particle into the sum like any other particle. Parent = daughter + particle, on both rows.

Physics · Beta-minus decay

Which way does the atomic number go?

A nucleus emits a beta-minus particle, ⁰₋₁e.

Which idea about the daughter's atomic number is closest to what you think?

It goes down by 1, because the particle is written with −1.It goes down, because something has left the nucleus.It goes up by 1, because a neutron changes into a proton.It stays the same, because the mass number stays the same.

How sure are you?

I'm sureI think soI'm guessing

It goes down by 1, because the particle is written with −1.

This is a common misconception

Test it with the rule: parent = daughter + particle. Bottom row: parent Z = daughter Z + (−1), so daughter Z = parent Z + 1. The −1 is a number in the sum. It is not an instruction to subtract.

It goes down, because something has left the nucleus.

This is a common misconception

Something does leave: a fast electron. But the electron appears when a neutron in the nucleus changes into a proton, so the nucleus ends up with one MORE proton. Protons are counted by the atomic number, and it rises.

It goes up by 1, because a neutron changes into a proton.

This matches the evidence

Yes. The conservation sum agrees: daughter Z + (−1) = parent Z, so the daughter's Z is one higher. One extra proton means a new element.

It stays the same, because the mass number stays the same.

This is a common misconception

The mass number does stay the same, but that is the top row. The atomic number is a separate total that counts protons. A neutron became a proton, so the bottom number rises by 1.

Don't subtract the −1. Put the particle in the sum and the daughter's atomic number comes out one higher.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

In nuclear notation the top number is the mass number (protons plus neutrons) and the bottom number is the atomic number (protons).
The atomic number decides which element a nucleus is, so a different atomic number means a different element.
In a nuclear equation the mass numbers total the same on both sides, and so do the atomic numbers.
Have a goA nucleus with mass number 20 decays into a daughter with mass number 16, plus one emitted particle. What mass number must the particle have?
4
The top row has to total 20 on both sides, so the particle's mass number is 20 − 16 = 4.
An alpha particle is a helium nucleus, ⁴₂He, so alpha emission takes 4 off the mass number and 2 off the atomic number.
Have a goYour friend says, "Alpha takes 4 off the top, so it must take 4 off the bottom too." Which two numbers actually fall, and by how much?
The mass number falls by 4 and the atomic number falls by 2.
Each row loses its own number from ⁴₂He: 4 is the alpha particle's mass number and 2 is its atomic number.
In beta-minus decay a neutron changes into a proton and a fast electron, written ⁰₋₁e, is emitted.
So beta-minus decay leaves the mass number unchanged and raises the atomic number by 1, which makes a new element.
Have a goA nucleus has atomic number 15 and emits a beta-minus particle. Write the bottom-row sum and solve it for the daughter.
15 = Z + (−1), so Z = 16
Parent 15 = daughter + (−1), so the daughter is 15 + 1 = 16; you do not subtract the −1.
Gamma emission only gets rid of extra energy, so the mass number and atomic number stay the same and it is the same element.
To find a missing nucleus or particle: total the top row, total the bottom row, then use the atomic number to name the element.
Check any answer by adding daughter plus emitted particle: the top and bottom totals must equal the parent's numbers.

The big picture

A nuclear equation is balanced when the mass numbers and the atomic numbers each total the same on both sides. Those two sums let you find any missing number, particle or daughter element for alpha, beta-minus and gamma emission.

Key points

1Mass numbers total the same on both sides, and atomic numbers total the same on both sides.

2Alpha: mass number −4, atomic number −2, new element.

3Beta-minus: mass number unchanged, atomic number +1, new element.

4Gamma: nothing changes, same element.

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Worked example

Problem

A polonium nucleus ²¹⁰₈₄Po (210 protons and neutrons, 84 protons) becomes lead-206 ²⁰⁶₈₂Pb by giving out one particle. Which particle?

⚠ Watch out

In beta-minus decay, subtracting the −1 and getting an atomic number one lower. The particle goes in the sum (parent = daughter + particle), so the daughter's atomic number is one higher.

🧠

Memory hook

Top row, bottom row, add them up. For beta-minus, take away a −1 and the nucleus is left one more positive, so the bottom number goes UP by one.

✓

Check yourself

Cover the page. Bismuth-210 (²¹⁰₈₃Bi) emits a beta-minus particle. What are the daughter's mass number and atomic number? Answer: 210 and 84.

Flashcards

(10)

What does the top number in nuclear notation show?

The mass number: the total number of protons and neutrons in the nucleus.

What does the bottom number show, and what does it decide?

The atomic number: the number of protons. It decides which element the nucleus is.

Which two totals must match on both sides of a nuclear equation?

The mass numbers (top row) and the atomic numbers (bottom row).

What is an alpha particle and how is it written?

A helium nucleus of 2 protons and 2 neutrons, written ⁴₂He.

By how much do the two numbers fall in alpha emission?

The mass number falls by 4 and the atomic number falls by 2, so a new element forms.

What happens inside the nucleus in beta-minus decay?

A neutron changes into a proton, and a fast electron is emitted.

After beta-minus decay, how do the two numbers compare with the parent's?

Top number unchanged, bottom number up by one. The particle is written ⁰₋₁e.

What does gamma emission do to the mass number and atomic number?

Neither changes. The nucleus only loses energy, so it is still the same element.

What are the steps for finding a missing daughter nucleus?

Total the top row, total the bottom row, subtract the known numbers, then name the element from its atomic number.

How do you check a nuclear equation is balanced?

Add the daughter and the emitted particle: the top and bottom totals must equal the parent's mass number and atomic number.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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One nucleus, three ways to decay

Beta-minus: you supply the missing steps

Which way does the atomic number go?

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