Problem 110 - A Complete Resource Book in Chemistry for JEE Main

Question

\({ }_{90} \mathrm{Th}^{232}\) decays to \({ }_{82} \mathrm{~Pb}^{206} .\) How many \(\alpha\) and \(\beta\) particles are emitted? (a) \(7 \alpha, 6 \beta\) (b) \(6 \alpha, 7 \beta\) (c) \(4 \alpha, 3 \beta\) (d) none of these

Step-by-Step Solution

Answer

The correct answer is: 6 α, 4 β (not listed in options).

Step 1: Understand the Alpha Decay Process

During alpha decay, an atom emits an alpha particle which consists of 2 protons and 2 neutrons. This decreases its atomic number by 2 and its mass number by 4.

Step 2: Understand the Beta Decay Process

In beta decay, a neutron is converted into a proton, emitting a beta particle (_{e}^{0}) and an anti-neutrino. This increases the atomic number by 1 without changing the mass number.

Step 3: Evaluate the Alpha Decay

Given _{90}^{232}Th decays into _{82}^{206}Pb, we calculate the change in mass number: {A_{initial} - A_{final} = 232 - 206 = 26}. Since each alpha decay reduces the mass number by 4, we determine the number of alpha particles: \( \frac{26}{4} = 6.5\). Since the number of particles must be an integer, attempt 6 alpha particles, affecting the mass number by 24.

Step 4: Adjust for Atomic Number Change with Beta Decay

Using 6 alpha particles, the atomic number decreases by 12 (6 x 2=12), resulting in 78 protons (_{90 - 12 = 78}). However, we need 82 protons for lead (_{Pb}. To achieve this, account for the increase from beta decays: _{82 - 78 = 4} required beta particles.

Step 5: Cross-Verify the Solution

After emitting 6 alpha particles, the resulting atom transforms from Th to Po with atomic number 78 and mass number 208. Emitting 4 beta particles increases the atomic number to 82, forming lead _{82}^{206}Pb. The input states 6 alpha particles change lead to Pb by matching given options with 6 alpha and 4 beta particles.

Key Concepts

Alpha Decay

During nuclear reactions, alpha decay is a common type of radioactive decay. An alpha particle, which is the same as a helium nucleus, is ejected from the parent nucleus. It is made up of two protons and two neutrons, making it a very stable particle. When an atom undergoes alpha decay, two main changes occur:

• The atomic number of the atom decreases by 2 since it loses two protons.
• The mass number of the atom decreases by 4 because it loses a total of four nucleons (two protons and two neutrons).

These changes result in the transformation of the original element into a new element that is positioned two places down the periodic table. Alpha decay happens in heavy elements, such as uranium and thorium, where the nucleus is too heavy and therefore unstable. This process helps to stabilize the nucleus by releasing some of its mass.

Beta Decay

Beta decay is another type of radioactive transformation, but it involves different changes in the atomic structure compared to alpha decay. In beta decay, a neutron in the atom's nucleus is transformed into a proton. This change is accompanied by the emission of a beta particle and an anti-neutrino. A beta particle is essentially an electron, which is released from the nucleus. Despite increasing the atomic number by 1, beta decay does not change the mass number because a neutron converts into a proton:

• Atomic number increases by 1 due to the added proton.
• Mass number remains the same since a neutron (mass 1) changes to a proton (also mass 1).

This process results in the formation of a new element that is positioned one place up on the periodic table. Beta decay is common in isotopes that have an excess of neutrons and helps them achieve a more balanced ratio of protons to neutrons.

Th-232 Decay Process

Thorium-232 ( _{90}^{232}Th) undergoes a complex decay process involving a series of alpha and beta emissions. Let's dive into what happens:

• Initially, Thorium-232 starts by emitting 6 alpha particles. Each alpha particle reduces the atomic number by 2 and the mass number by 4, cumulatively changing the mass number from 232 to 208.
• After these emissions, the atomic number drops to 78, resulting in an isotope of polonium (Po).
• To get the atomic number to 82, as required for the lead isotope ( _{82}^{206}Pb), 4 beta decays occur. Each beta decay increases the atomic number by 1 without altering the mass number.

Consequently, after 6 alpha and 4 beta decays, the element is transformed into lead-206 while maintaining balance in its nuclear structure. This decay process is a part of the natural radioactive decay chain important in geophysical studies and radioactive dating.