The nucleon conservation principle in nuclear processes

Nuclear processes involve changes within the nucleus of an atom, where particles such as protons and neutrons rearrange or are emitted. A key rule governing these changes is the nucleon conservation principle. Nucleons are the particles in the nucleus, specifically protons and neutrons.

This principle states that the total number of nucleons remains constant during any nuclear process. In other words, the sum of protons plus neutrons before the process equals the sum after, even as particles redistribute among the products.

How nucleon conservation works

• Total nucleons constant - If the original nucleus has a certain mass number (total protons plus neutrons), the combined mass numbers of all products must match it.
• Redistribution of particles - During decay, nucleons may shift from the parent nucleus to emitted particles, but none are created or destroyed.
• Application to equations - This principle ensures nuclear equations balance on both sides for mass numbers and atomic numbers (number of protons).

This conservation helps predict the outcomes of nuclear decays and maintains the balance in written equations.

Writing nuclear equations for alpha decay

Alpha decay is a nuclear process where an unstable nucleus emits an alpha particle to become more stable. An alpha particle is a helium nucleus, denoted as ${}_2^4\alpha$ or ${}_2^4\text{He}$, consisting of 2 protons and 2 neutrons.

In alpha decay, the parent nucleus loses 4 nucleons (2 protons and 2 neutrons), following the nucleon conservation principle. This results in subtracting 4 from the mass number (A) and 2 from the atomic number (Z) to form the daughter nucleus.

Steps to write an alpha decay equation

1. Identify the parent nucleus, written as ${}_Z^A\text{X}$, where X is the element symbol from the periodic table.
2. Subtract 4 from A and 2 from Z to get the daughter nucleus ${}_{Z-2}^{A-4}\text{Y}$.
3. Add the alpha particle ${}_2^4\alpha$ as a product.
4. Ensure the equation balances: total A and Z on both sides must match.
5. Use the periodic table to find Y's symbol based on the new Z.

This process conserves nucleons as the alpha particle accounts for the lost mass and charge.

Worked example - Writing an alpha decay equation

Write the nuclear equation for the alpha decay of uranium-238 (${}_{92}^{238}\text{U}$).

Step 1: Identify the parent nucleus

The parent is ${}_{92}^{238}\text{U}$, with A = 238 and Z = 92.

Step 2: Apply changes for alpha decay

Subtract 4 from A: 238 - 4 = 234

Subtract 2 from Z: 92 - 2 = 90

Step 3: Write the equation

${}_{92}^{238}\text{U}{\to }_{90}^{234}\text{Th}{+}_2^4\alpha$

Step 4: Verify using periodic table

Element with Z = 90 is thorium (Th). The equation balances: left side A = 238, Z = 92; right side A = 234 + 4 = 238, Z = 90 + 2 = 92.

Writing nuclear equations for beta decay

Beta decay occurs when an unstable nucleus emits a beta particle to achieve stability. A beta particle is an electron, denoted as ${}_{-1}^0\beta$ or ${}_{-1}^0\text{e}$.

In this process, a neutron in the nucleus transforms into a proton plus an electron. The electron is emitted, increasing the atomic number by 1 while the mass number stays the same, as the electron has negligible mass.

Steps to write a beta decay equation

1. Identify the parent nucleus ${}_Z^A\text{X}$.
2. Keep A the same and add 1 to Z for the daughter nucleus ${}_{Z+1}^A\text{Y}$.
3. Add the beta particle ${}_{-1}^0\beta$ as a product.
4. Balance the equation: total A remains A on both sides; Z on right is (Z+1) + (-1) = Z.
5. Use the periodic table to identify Y based on Z+1.

Nucleon conservation holds because the neutron-to-proton change keeps the total nucleons constant.

Worked example - Writing a beta decay equation

Write the nuclear equation for the beta decay of carbon-14 (${}_6^{14}\text{C}$).

Step 1: Identify the parent nucleus

The parent is ${}_6^{14}\text{C}$, with A = 14 and Z = 6.

Step 2: Apply changes for beta decay

Keep A = 14.

Add 1 to Z: 6 + 1 = 7.

Step 3: Write the equation

${}_6^{14}\text{C}{\to }_7^{14}\text{N}{+}_{-1}^0\beta$

Step 4: Verify using periodic table

Element with Z = 7 is nitrogen (N). The equation balances: left side A = 14, Z = 6; right side A = 14 + 0 = 14, Z = 7 + (-1) = 6.

Writing nuclear equations for gamma decay

Gamma decay involves the release of gamma radiation from an excited nucleus to reach a lower energy state. Gamma radiation is high-energy electromagnetic waves, denoted as ${}_0^0\gamma$, with no mass or charge.

This process does not change the mass number or atomic number, as it only releases energy without altering the number of protons or neutrons.

Steps to write a gamma decay equation

1. Identify the excited parent nucleus, often shown with an asterisk (e.g., ${}_Z^A{\text{X}}^{\ast }$).
2. The daughter nucleus is the same as the parent: ${}_Z^A\text{X}$.
3. Add the gamma ray ${}_0^0\gamma$ as the product.
4. The equation balances automatically since there are no changes to A or Z.
5. No need to change the element symbol, as Z remains the same.

Nucleon conservation is maintained because no particles with mass are emitted.

Worked example - Writing a gamma decay equation

Write the nuclear equation for the gamma decay of excited technetium-99 (${}_{43}^{99}{\text{Tc}}^{\ast }$).

Step 1: Identify the parent nucleus

The excited parent is ${}_{43}^{99}{\text{Tc}}^{\ast }$, with A = 99 and Z = 43.

Step 2: Apply changes for gamma decay

No change to A or Z.

Step 3: Write the equation

${}_{43}^{99}{\text{Tc}}^{\ast }{\to }_{43}^{99}\text{Tc}{+}_0^0\gamma$

Step 4: Verify using periodic table

The element remains technetium (Tc) since Z = 43. The equation balances: left side A = 99, Z = 43; right side A = 99 + 0 = 99, Z = 43 + 0 = 43.

Writing nuclear equations for neutron emission

Neutron emission is a nuclear process where an unstable nucleus releases a neutron to become more stable. A neutron is denoted as ${}_0^1\text{n}$, with mass number 1 and atomic number 0.

This emission decreases the mass number by 1 while keeping the atomic number the same, as no protons are involved.

Steps to write a neutron emission equation

1. Identify the parent nucleus ${}_Z^A\text{X}$.
2. Subtract 1 from A and keep Z the same for the daughter nucleus ${}_Z^{A-1}\text{Y}$.
3. Add the neutron ${}_0^1\text{n}$ as a product.
4. Balance the equation: total A on right is (A-1) + 1 = A; Z remains Z.
5. Use the periodic table to confirm Y, which has the same Z.

This follows nucleon conservation, as the emitted neutron accounts for the lost mass.

Worked example - Writing a neutron emission equation

Write the nuclear equation for the neutron emission of helium-5 (${}_2^5\text{He}$).

Step 1: Identify the parent nucleus

The parent is ${}_2^5\text{He}$, with A = 5 and Z = 2.

Step 2: Apply changes for neutron emission

Subtract 1 from A: 5 - 1 = 4.

Keep Z = 2.

Step 3: Write the equation

${}_2^5\text{He}{\to }_2^4\text{He}{+}_0^1\text{n}$

Step 4: Verify using periodic table

Element with Z = 2 remains helium (He). The equation balances: left side A = 5, Z = 2; right side A = 4 + 1 = 5, Z = 2 + 0 = 2.

Using the periodic table to identify resulting elements

The periodic table organizes elements by atomic number (Z), which is the number of protons. In nuclear equations, after calculating the new Z for the daughter nucleus, refer to the periodic table to find the corresponding element symbol.

Key steps for identification:

• Determine the new Z from the decay rules.
• Locate the element with that Z on the periodic table.
• Write the symbol for the daughter element in the equation.
• Remember that mass number (A) does not affect the element identity—only Z does.

This ensures accurate representation of the products while respecting nucleon conservation.