Problem 69 - A Complete Resource Book in Chemistry for JEE Main

Question

In natural radioactive disintegration, U-238 emits one \(\alpha\) and two \(\beta\) and then five \(\alpha\) particle successively. The end product obtained is (a) \({ }_{82} \mathrm{~Pb}^{218}\) (b) \({ }_{82} \mathrm{~Pb}^{214}\) (c) \({ }_{84} \mathrm{~Pb}^{218}\) (d) \({ }_{82} \mathrm{~Pb}^{216}\)

Step-by-Step Solution

Answer

The end product after decay is
${ }_{82}
Pb^{214}$.

Step 1: Understand
alpha and beta decay

In radioactive decay, an
alpha (
α) particle consists of 2 protons and 2 neutrons. When a nucleus emits an
α particle, the atomic number decreases by 2 and the mass number decreases by 4. A beta (
β) particle is an electron emitted from the nucleus. During
β decay, a neutron changes into a proton, increasing the atomic number by 1, while the mass number remains unchanged.

Step 2: Initial particle transformation after decays

Start with the original element, uranium-238: The atomic number is 92, and the mass number is 238. After emitting one
α particle, the new atomic number becomes 92 - 2 = 90, and the mass number becomes 238 - 4 = 234. After two
β decays, the atomic number increases by 2 (1 per decay), so it becomes 90 + 2 = 92, and the mass number remains 234.

Step 3: Follow with five alpha decays

Each
α decay decreases the atomic number by 2 and the mass number by 4. Therefore, five
α decays affect the atom as follows: Atomic number: 92 - (5 × 2) = 82. Mass number: 234 - (5 × 4) = 214.

Step 4: Identify the element

An atomic number of 82 corresponds to the element lead (Pb) on the periodic table. Combining this with the mass number 214, the final product is
${ }_{82}
Pb^{214}$.

Key Concepts

Alpha decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. This process reduces the mass number of the original atom by 4 and the atomic number by 2. In simple terms, the atom loses the equivalent of a helium nucleus, which is what an alpha particle is.

• Mass number decreases by 4.
• Atomic number decreases by 2.

Alpha decay is common in heavier elements, like Uranium, as it helps them achieve a more stable configuration. Over time, this decay chain transforms the element into another, more stable element.

Beta decay

Beta decay involves the transformation of a neutron into a proton within the nucleus, accompanied by the emission of a beta particle. This beta particle is a high-energy, fast-moving electron. Unlike alpha decay, beta decay changes the atomic number but leaves the mass number unchanged as the process involves a conversion within the nucleus.

• Mass number remains the same.
• Atomic number increases by 1.

Beta decay is essential for balancing nuclear reactions by altering the neutron-to-proton ratio, stabilizing an otherwise unstable nucleus. This form of decay is fundamental to many processes in nuclear physics and Earth’s natural radiogenic heating.

Uranium-238

Uranium-238 is a common isotope of uranium, with an atomic number of 92 (meaning it has 92 protons) and a mass number of 238. It is essential for understanding nuclear physics and the natural processes of radioactive decay, as it represents one of the heaviest natural elements and a starting point for many decay chains.

• Atomic number: 92
• Mass number: 238

U-238 undergoes alpha decay most frequently, shedding alpha particles before ultimately decaying into a stable element over millions of years. It's an important fuel in nuclear reactors and plays a vital role in dating ancient geological formations.

Lead-214

Lead-214 is an isotope of lead that results from the sequential decay of uranium-238. Specifically, it is formed at the end of the described decay series where five alpha decays and two beta decays from the original uranium-238 transform it into lead-214.

• Atomic number: 82
• Mass number: 214

Lead-214 itself is radioactive, decaying quickly through additional beta decay processes to eventually reach stability. It is an intermediary step in the uranium decay chain, highlighting the transformation pathways of heavy metals through radioactive processes. Understanding these pathways is critical for nuclear science and dating methods.