Question

Francium has an atomic number of 87 . Write the nuclear equation for the alpha particle emission of francium-212. What is the daughter isotope?

Short answer

Fr-212 decays into At-208 via alpha decay ( \[ ^{212}_{87}Fr \rightarrow ^{208}_{85}At + ^{4}_{2}He \] ).

Step-by-step solution

Identify the Parent Isotope

Francium-212 means we are dealing with a Francium (Fr) isotope with a mass number of 212. The atomic number of Francium is 87, which means it has 87 protons.

Understand Alpha Particle Emission

An alpha particle consists of 2 protons and 2 neutrons, which means when a nucleus emits an alpha particle, its atomic number decreases by 2 and its mass number decreases by 4.

Write the Nuclear Equation

Start with the parent isotope on the left side of the equation: \[ ^{212}_{87}Fr \rightarrow ^{208}_{85}X + ^{4}_{2}He \]Where \(X\) represents the daughter isotope that we need to identify. The alpha particle emitted is represented by \(^{4}_{2}He\).

Determine the Daughter Isotope

Subtract the alpha particle from the parent isotope: - Mass number: 212 - 4 = 208 - Atomic number: 87 - 2 = 85 With an atomic number of 85, the daughter isotope is Astatine (At).

State the Final Nuclear Equation

The complete nuclear equation showing the alpha decay is:\[ ^{212}_{87}Fr \rightarrow ^{208}_{85}At + ^{4}_{2}He \]This indicates Francium-212 decays into Astatine-208 by alpha particle emission.

Key concepts

Nuclear Equation

Nuclear equations are used to represent changes in the nucleus of an atom during nuclear reactions. These are not the same as chemical equations that describe changes in electron arrangements. Nuclear equations must account for both atomic numbers and mass numbers, ensuring that the total number of protons and the total mass is conserved on both sides of the equation.

In the process of alpha decay, a nucleus loses an alpha particle, which affects both its atomic and mass numbers. For instance, the nuclear equation for the alpha decay of Francium-212 can be written as follows:

• The left side begins with the parent isotope: \(^ {212}_{87}Fr\)
• On the right side, we find the daughter isotope and the ejected alpha particle: \(^ {208}_{85}X + ^{4}_{2}He\)

The equation reflects the conservation of mass and charge—a fundamental law in nuclear reactions. You can verify this by adding up the atomic and mass numbers on each side.

Daughter Isotope

In nuclear reactions, the term "daughter isotope" refers to the new isotope formed after a nucleus undergoes decay. The daughter isotope has different nuclear properties than the original or "parent" isotope.

During an alpha decay, the parent isotope loses an alpha particle, which results in a decrease in both its atomic and mass numbers. Let's look at the example of Francium-212 undergoing alpha decay. Here's what happens:

• The original parent isotope has an atomic number of 87 and a mass number of 212.
• The loss of an alpha particle (2 protons and 2 neutrons) decreases the atomic number by 2 and the mass number by 4.
• This results in a daughter isotope with an atomic number of 85 and a mass number of 208, which is Astatine-208.

The transformation highlights how radioactive decay alters the identity of an element, producing new isotopes with distinct characteristics.

Alpha Particle Emission

Alpha particle emission is a type of radioactive decay where an unstable nucleus releases an alpha particle, consisting of 2 protons and 2 neutrons. This process results in the creation of a new element with a smaller atomic and mass number.

When an alpha particle is emitted, it is essentially a helium nucleus \(^{4}_{2}He\). The ejection of this small cluster of nucleons has significant effects on the decaying nucleus:

• The atomic number decreases by 2, as the nucleus loses 2 protons.
• The mass number decreases by 4, due to the loss of a total of 4 nucleons (2 protons + 2 neutrons).

This change stabilizes the nucleus by shifting it into a lower energy state. Alpha particle emission is commonly observed in heavy elements where reducing the number of protons and neutrons helps increase stability. The emitted alpha particle is a key component in nuclear reactions, playing a crucial role in various applications, including nuclear medicine and power generation.