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 is reduced by 4 units; option (a) is correct.

Step 1: Understanding Radioactive Decay

Radioactive decay involves the emission of particles. An \( \alpha \) particle consists of 2 protons and 2 neutrons, leading to a decrease in mass number by 4 and atomic number by 2. A \( \beta \) particle emission, which is an electron, increases the atomic number by 1 (no change in mass number). Since two \( \beta \) particles are emitted, they raise the atomic number by 2.

Step 2: Calculating Mass Number Change

When an \( \alpha \) particle is emitted, the mass number reduces by 4 units. Emitting two \( \beta \) particles does not alter the mass number because beta decay only affects the atomic number. Hence, after all emissions, the mass number decreases by 4 as a result of the alpha decay only.

Step 3: Evaluating the Options

Given options are (a) reduced by 4 units, (b) remains the same, (c) reduced by 2 units, and (d) increased by 2 units. Since the mass number underwent a net reduction of 4 units, option (a) 'is reduced by 4 units' is correct.

Key Concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an atom emits an alpha particle. An alpha particle is composed of two protons and two neutrons, essentially making it a helium nucleus. When a radioactive atom undergoes alpha decay, it loses this cluster of four nuclear particles.

This process results in a few important changes:

• The **mass number** of the atom decreases by 4. This is because 2 protons and 2 neutrons – totaling 4 particles – are ejected from the nucleus.
• The **atomic number** decreases by 2, since 2 protons are lost.

Alpha decay typically occurs in heavier elements, and it makes the resulting atom more stable by reducing the nuclear size. Due to the loss of these particles, the atom transforms into a different element. For example, when uranium-238 emits an alpha particle, it becomes thorium-234.

Beta Decay

Beta decay is another common type of radioactive decay, and it involves the emission of a beta particle. Unlike alpha particles, a beta particle is simply a high-energy, fast-moving electron. There are two types of beta decay: beta-minus decay and beta-plus decay. Here, we focus on beta-minus decay, which is more common in nature.

During beta-minus decay:

• A **neutron** in the nucleus is converted into a **proton** and an **electron** (the beta particle).
• The newly formed electron is ejected from the atom.
• The **mass number** remains unchanged because it depends on the total count of protons and neutrons, which does not alter.
• The **atomic number** increases by 1 since a neutron has been replaced with a proton.

This change transforms the atom into a new element with one higher atomic number, but the same mass number. For instance, when carbon-14 undergoes beta-minus decay, it turns into nitrogen-14.

Mass Number Change

In radioactive decay, the mass number of an element can change as a result of particle emission. The mass number is the sum of protons and neutrons in the nucleus.

When a radioactive element undergoes alpha decay, the mass number decreases by 4 because both protons and neutrons are lost in the emitted alpha particle. However, during beta decay, only a neutron is converted into a proton, and since protons and neutrons each contribute equally to the mass number, the mass number does not change.

To understand the impact on mass number:

• **Alpha Decay**: Mass number decreases by 4.
• **Beta Decay**: Mass number remains the same.

In scenarios where an element undergoes one alpha decay and two beta decays sequentially, the total change in mass number will solely depend on the alpha decay, resulting in a reduction of 4 from the original mass number. Thus, the mass number change in such a process is a decrease by 4 units.