Nuclear Equations for Fission & Fusion (WJEC GCSE Physics): Revision Note

A possible nuclear equation for the fission of uranium-235 is

${}_{92}{}^{235}\mathrm{U}+{}_0{}^1\mathrm{n}\to {}_{37}{}^{96}\mathrm{Rb}+{}_{55}{}^{137}\mathrm{Cs}+\mathrm{N}{}_0{}^1\mathrm{n}$

Calculate the number of neutrons N released in this reaction.

Answer:

Step 1: Calculate the nucleon number on the left side of the equation

235 + 1 = 236

Step 2: Calculate the nucleon number on the right side of the equation 

96 + 138 + (N × 1) = 233 + N

Step 3: Equate the nucleon number for both sides of the equation 

236 = 233 + N

Step 4: Rearrange for the number of neutrons, N

N = 236 – 233 = 3

One of the nuclear fusion reactions that occurs in the Sun is shown below.

${}_{.....}{}^{.....}\mathrm{H}+{}_{.....}{}^{.....}\mathrm{H}\to {}_2{}^3\mathrm{He}+\hspace{0.17em}\mathrm{\gamma }$

Complete the equation.

Answer:

Step 1: Recall the proton number for hydrogen and the meaning of isotope

• Isotopes are elements with the same proton number but different nucleon numbers

• Hydrogen has a proton number of 1

• So, the bottom number for both hydrogen nuclei is 1

Step 2: Determine the nucleon numbers of the hydrogen isotopes

• The total nucleon number on the right side of the equation is 3, as gamma is an electromagnetic wave so does not have a nucleon or proton number

• The hydrogen nuclei on the left side are isotopes

• Therefore, their nucleon numbers must be 1 and 2

Step 3: Write the equation out in full and check both sides

${}_1{}^1\mathrm{H}+{}_1{}^2\mathrm{H}\to {}_2{}^3\mathrm{He}+\hspace{0.17em}\mathrm{\gamma }$

• Nucleon numbers: 1 + 2 = 3 + 0

• Proton numbers: 1 + 1 = 2 + 0

• The numbers balance, so the equation must be correct

The diagram below shows an example of a nuclear fusion reaction in which two isotopes of helium $\left(\mathrm{He}\right)$ fuse together to make a beryllium-7 $\left({}_4{}^7\mathrm{Be}\right)$ nucleus plus the emission of a gamma ray.

Write a balanced nuclear equation for this fusion reaction.

Answer:

Step 1: Write a word equation using the information in the question

• Underline or highlight the keywords in the question:

  "Two isotopes of helium fuse together to make a beryllium-7 nucleus plus the emission of a gamma ray"

• Write a word equation for the reaction:

helium + helium → beryllium-7 + gamma

Step 2: Work out the symbols for the helium isotopes

• The ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ notation for beryllium-7 is ${}_4{}^7\mathrm{Be}$

  • This means it contains 4 protons and 3 neutrons

  • Using the diagram, we can deduce the light particles are protons and the dark particles are neutrons

• Isotopes are elements with the same proton number but different nucleon numbers

• So, both helium nuclei must have a proton number of 2

• The two helium isotopes are therefore: 

  • Helium-3:  ${}_2{}^3\mathrm{He}$ (2 protons, 1 neutron)

  • Helium-4:  ${}_2{}^4\mathrm{He}$ (2 protons, 2 neutrons)

• Gamma particles have no mass or charge so have nucleon and proton numbers of 0

Step 3: Write the balanced nuclear equation using the correct symbols

${}_2{}^3\mathrm{He}+{}_2{}^4\mathrm{He}\to {}_4{}^7\mathrm{Be}+{}_0{}^0\mathrm{\gamma }$

• Nucleon numbers: 3 + 4 = 7 + 0

• Proton numbers: 2 + 2 = 4 + 0

• The numbers balance, so the equation must be correct

The table shows some information about different nuclei involved in a nuclear fission reaction.

A nucleus of uranium undergoes fission when bombarded with a slow-moving neutron (n) causing it to split into the daughter nuclei barium and krypton plus the release of further neutrons.

Write a balanced nuclear equation for this fission reaction.

$.........+.........\to .........+.........+.........$

Answer:

Step 1: Write a word equation using the information in the question

• Underline or highlight the keywords in the question which tell us about the nuclei on the left-hand side (LHS):

  "A nucleus of uranium undergoes fission when bombarded with a slow-moving neutron"

• Underline or highlight the keywords in the question which tell us about the nuclei on the right-hand side (RHS):

  "causing it to split into the daughter nuclei barium and krypton plus the release of further neutrons"

• Write a word equation for the reaction:

uranium + neutron → barium + krypton + neutrons

Step 2: Determine the correct symbols for each nucleus or particle

• We need to write each nucleus or particle in ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ notation

• It can be useful to draw an extra row and column onto the table to do this (green indicates the changes made to the table):

Step 3: Write the nuclear equation using the symbols

${}_{92}{}^{235}\mathrm{U}+{}_0{}^1\mathrm{n}\to {}_{56}{}^{144}\mathrm{Ba}+{}_{36}{}^{89}\mathrm{Kr}+{}_0{}^1\mathrm{n}$

Step 4: Balance the equation by checking the total nucleon and proton numbers on each side

• Total proton number:

  • On the LHS: 92 + 0 = 92

  • On the RHS: 56 + 36 + 0 = 92

• The total proton number is the same on both sides

• Total nucleon number:

  • On the LHS: 235 + 1 = 236

  • On the RHS: 144 + 89 + 1 = 234

• There is a difference of 2, and the question states there is a "release of further neutrons"

• This means there must be 2 extra neutrons released i.e. 3 neutrons in total

• To represent this, we put a 3 in front of the neutron symbol on the RHS, so, the fully balanced equation is:

${}_{92}{}^{235}\mathrm{U}+{}_0{}^1\mathrm{n}\to {}_{56}{}^{144}\mathrm{Ba}+{}_{36}{}^{89}\mathrm{Kr}+3{}_0{}^1\mathrm{n}$