List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option. List-I List-II (P) 𝑈 → 91𝑃𝑎 234 92 238 (1) one 𝛼 particle and one 𝛽 + particle (Q) 𝑃𝑏 → 82𝑃𝑏 210 82 214 (2) three 𝛽 − particles and one 𝛼 particle (R) 𝑇𝑙 → 82𝑃𝑏 206 81 210 (3) two 𝛽 − particles and one 𝛼 particle (S) 𝑃𝑎 → 88𝑅𝑎 224 91 228 (4) one 𝛼 particle and one 𝛽 − particle (5) one 𝛼 particle and two 𝛽 + particles (A) 𝑃 → 4,𝑄 → 3, 𝑅 → 2, 𝑆 → 1 (B) 𝑃 → 4,𝑄 → 1, 𝑅 → 2, 𝑆 → 5 (C) 𝑃 → 5,𝑄 → 3, 𝑅 → 1, 𝑆 → 4 (D) 𝑃 → 5,𝑄 → 1, 𝑅 → 3, 𝑆 → 2

 To solve this problem, we need to understand the radioactive decay processes and the particles emitted during each decay. Let's analyze each decay process in List-I and match it with the appropriate emitted particles in List-II.

List-I:

• (P) ${}_{92}^{238}U{\to }_{91}^{234}Pa$

• (Q) ${}_{82}^{214}Pb{\to }_{82}^{210}Pb$

• (R) ${}_{81}^{210}Tl{\to }_{82}^{206}Pb$

• (S) ${}_{91}^{228}Pa{\to }_{88}^{224}Ra$

List-II:

1. One α particle and one β⁺ particle

2. Three β⁻ particles and one α particle

3. Two β⁻ particles and one α particle

4. One α particle and one β⁻ particle

5. One α particle and two β⁺ particles

Analysis:

1. Decay (P): ${}_{92}^{238}U{\to }_{91}^{234}Pa$

   • Uranium-238 decays to Protactinium-234.

   • The atomic number decreases by 1 (92 to 91), indicating the emission of a β⁺ particle (positron).

   • The mass number decreases by 4 (238 to 234), indicating the emission of an α particle.

   • Match: (1) One α particle and one β⁺ particle.

2. Decay (Q): ${}_{82}^{214}Pb{\to }_{82}^{210}Pb$

   • Lead-214 decays to Lead-210.

   • The atomic number remains the same (82), indicating no β decay.

   • The mass number decreases by 4 (214 to 210), indicating the emission of an α particle.

   • Match: (4) One α particle and one β⁻ particle.

3. Decay (R): ${}_{81}^{210}Tl{\to }_{82}^{206}Pb$

   • Thallium-210 decays to Lead-206.

   • The atomic number increases by 1 (81 to 82), indicating the emission of a β⁻ particle.

   • The mass number decreases by 4 (210 to 206), indicating the emission of an α particle.

   • Match: (3) Two β⁻ particles and one α particle.

4. Decay (S): ${}_{91}^{228}Pa{\to }_{88}^{224}Ra$

   • Protactinium-228 decays to Radium-224.

   • The atomic number decreases by 3 (91 to 88), indicating the emission of three β⁺ particles.

   • The mass number decreases by 4 (228 to 224), indicating the emission of an α particle.

   • Match: (2) Three β⁻ particles and one α particle.

Correct Option:

• (A) $P\to 4,Q\to 3,R\to 2,S\to 1$

However, based on the analysis:

• $P\to 1$

• $Q\to 4$

• $R\to 3$

• $S\to 2$

Thus, the correct option is:

• (A) $P\to 4,Q\to 3,R\to 2,S\to 1$ is incorrect.

• The correct matching is not listed in the provided options.

Final Answer: None of the provided options correctly match the decays with the emitted particles based on the analysis.