Question

Assume that Bismuth- 213 decays to a stable nucleus by a series of two alpha and two beta emissions. What is the stable nucleus that is formed?

Short answer

The stable nucleus formed after Bismuth-213 undergoes a series of two alpha and two beta emissions is Thallium-205 (Tl-205).

Step-by-step solution

Understand Alpha Emission

In an alpha emission, a nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. As a result, the atomic number (Z) of the nucleus decreases by 2, and the mass number (A) decreases by 4.

Understand Beta Emission

In a beta emission, a nucleus emits a beta particle, which is an electron (e^-). This occurs when a neutron in the nucleus is converted into a proton. Consequently, the atomic number (Z) of the nucleus increases by 1, and the mass number (A) remains the same as the total number of nucleons (protons + neutrons) has not changed.

Apply Alpha Emissions twice

We'll start with Bismuth-213. The atomic number of Bismuth is 83, and its mass number is 213. After the first alpha emission: New atomic number (Z) = 83 - 2 = 81 New mass number (A) = 213 - 4 = 209 After the second alpha emission: New atomic number (Z) = 81 - 2 = 79 New mass number (A) = 209 - 4 = 205

Apply Beta Emissions twice

Now, we apply two beta emissions to the nucleus: After the first beta emission: New atomic number (Z) = 79 + 1 = 80 New mass number (A) = 205 (unchanged) After the second beta emission: New atomic number (Z) = 80 + 1 = 81 New mass number (A) = 205 (unchanged)

Identify the stable nucleus

The final nucleus has an atomic number (Z) of 81 and a mass number (A) of 205. From the periodic table, we can identify the element with an atomic number of 81 as Thallium (Tl). Therefore, the stable nucleus formed is Thallium-205 (Tl-205).

Key concepts

Alpha Emission

Alpha emission is a type of nuclear decay where the unstable nucleus releases an alpha particle. An alpha particle is essentially a helium nucleus, consisting of 2 protons and 2 neutrons. This process reduces the atomic number of the element by 2 and decreases the mass number by 4. For instance, if an element like Bismuth-213 undergoes alpha decay, its new atomic number will be 81 after the first emission. By shedding a second alpha particle, it will drop again, reaching an atomic number of 79 with a mass number of 205.
It's important to note that this loss of protons effectively transforms the element into a different chemical element due to the change in atomic number.

• Alpha particle: 2 protons + 2 neutrons
• Decreases atomic number by: 2
• Decreases mass number by: 4

Beta Emission

Beta emission is another common type of nuclear decay, where a neutron in an unstable nucleus is transformed into a proton while emitting a beta particle, which is an electron. During this process, the atomic number of the element increases by 1, while the mass number remains unchanged because the number of nucleons (protons plus neutrons) stays the same. This change is crucial as it affects the identity of the element. For example, after Bismuth-213 undergoes two alpha emissions and then two beta emissions, each beta emission adds one proton, transforming the element into Thallium-205.

• Beta particle: Electron (e^-)
• Increases atomic number by: 1
• Mass number: Unchanged

Bismuth-213

Bismuth-213 is a radioactive isotope of Bismuth with an atomic number of 83 and a mass number of 213. This isotope is unstable due to its high atomic weight and is prone to nuclear decay processes to achieve stability.
The decay process of Bismuth-213 involves a combination of alpha and beta emissions to reach a stable state. By first undergoing two alpha emissions, Bismuth-213 shifts to an element with a lower atomic number and mass number. This initial decay reduces its atomic number from 83 to 79 and its mass from 213 to 205.

• Initial atomic number: 83
• Initial mass number: 213
• Decay involves: 2 alpha + 2 beta emissions

Thallium-205

Thallium-205 is a stable isotope of the element Thallium, which has an atomic number of 81 and a mass number of 205. In this case, it is the end product of Bismuth-213's decay process that involves the emission of both alpha and beta particles. This sequence of transformations leads to the production of Thallium-205 from Bismuth-213, ensuring the new nucleus is stable.
Thallium-205 doesn't undergo further radioactive decay under normal conditions, representing a stable conclusion to the initial instability posed by Bismuth-213.

• Final atomic number: 81
• Final mass number: 205
• End product of: Bismuth-213 decay