Problem 41 - A Complete Resource Book in Chemistry for JEE Main

Question

When a radioactive element emits successively one \(\alpha\). particle and two \(\beta\) particles, the mass number of the daughter element (a) is reduced by 4 units (b) remains the same (c) is reduced by 2 units (d) is increased by 2 units

Step-by-Step Solution

Answer

The mass number of the daughter element is reduced by 4 units.

Step 1: Understanding Alpha Decay

In alpha decay, the parent nucleus emits an alpha particle which consists of 2 protons and 2 neutrons. This results in the reduction of the atomic number by 2 and the mass number by 4.

Step 2: Effect of Alpha Decay

After the emission of an alpha particle, the mass number is reduced by 4 units. If the original mass number is A, it becomes \(A - 4\).

Step 3: Understanding Beta Decay

In beta decay, a neutron in the nucleus is converted into a proton, causing the emission of a beta particle (an electron). This increases the atomic number by 1 but does not change the mass number.

Step 4: Effect of Two Beta Decays

For two beta decays, the atomic number increases by 2 (1 per beta decay), but the mass number remains unchanged. Therefore, the mass number stays \(A - 4\) after the successive beta decays.

Step 5: Resulting Mass Number after Successive Emissions

Considering both the alpha decay and the two beta decays, the final mass number remains at \(A - 4\). This means the mass number is reduced by 4 units from its original value.

Key Concepts

Alpha Decay

When a radioactive element undergoes alpha decay, it emits an alpha particle. An alpha particle is made up of two protons and two neutrons, which equates to a helium nucleus. Because this emission involves protons and neutrons, both the atomic number and the mass number of the parent atom change. The atomic number, which determines the element's identity, decreases by 2. This is because you're essentially subtracting two protons. The mass number, on the other hand, decreases by 4, given that the total mass removed equals the combined mass of the 2 protons and 2 neutrons.

• Alpha decay leads to a transformation into a new element with a lower atomic number.
• Mass number is significantly impacted, dropping by 4 units.
• Energy is also released, as radioactivity is the process of unstable nuclei releasing energy in an attempt to reach a stable state.

This makes alpha decay a crucial process in understanding how radioactive elements transform over time as they seek stability.

Beta Decay

Beta decay takes a different approach compared to alpha decay. In beta decay, a neutron from within the nucleus is transformed into a proton. During this transformation, a beta particle, which is an electron, is emitted. What makes beta decay interesting is that it alters the atomic number without affecting the mass number.
Here's what happens:

• The atomic number of the element increases by 1 for each beta decay. This is because a neutron converting to a proton adds one more proton to the nucleus.
• However, the mass number remains unchanged. This is due to the fact that the total number of nucleons (protons and neutrons) doesn’t change; only their arrangement does.

In the context of two successive beta decays, the atomic number increases by 2, while the mass number remains the same as it was post-alpha decay.

Mass Number Changes

The mass number in an atom tells us the total number of protons and neutrons within its nucleus. It is a critical factor in understanding the changes in isotopes resulting from radioactive decay.
Here's a step-by-step breakdown of how the mass number is impacted by radioactive decay:

• During alpha decay, the mass number decreases by 4 units. This is due to the loss of two protons and two neutrons, which together make an alpha particle.
• Beta decay, on the other hand, does not affect the mass number. Although it changes neutrons into protons, the total count of nucleons remains the same, thereby leaving the mass number untouched.
• In the scenario where one alpha decay and two beta decays occur successively, the overall effect on the mass number is a decrease of 4 units from its starting value.

Understanding these changes helps to predict the resulting element and its isotopic nature after it has undergone radioactive decay processes.