Question

How many alpha and beta particles are emitted when Uranium ₉₂U²³⁸ decays to lead ₈₂Pb²⁰⁶

• A. 3 alpha particles and 5 beta particles
• B. 6 alpha particles and 4 beta particles
• C. 4 alpha particles and 5 beta particles
• D. 8 alpha particles and 6 beta particles

Answer 1

The Correct Option is D

To determine the number of alpha and beta particles emitted when Uranium ^{238}_{92}\text{U} decays to Lead ^{206}_{82}\text{Pb}, we need to understand the decay process and use the relevant equations.

Understanding the Decay Process

1. **Alpha Decay**: In alpha decay, an element emits an alpha particle, which consists of 2 protons and 2 neutrons (equivalent to a Helium nucleus). As a result, the atomic number of the element decreases by 2, and the mass number decreases by 4. An alpha particle is represented by ^{4}_{2}\text{He}.

2. **Beta Decay**: In beta decay, a neutron is converted into a proton, and a beta particle (an electron, \beta^{-}) is emitted. The atomic number increases by 1, while the mass number remains unchanged.

Equation for the Decay

The decay of uranium-238 to lead-206 can be represented by the equation:

{}^{238}_{92}\text{U} \rightarrow {}^{206}_{82}\text{Pb} + x\cdot{}^{4}_{2}\text{He} + y\cdot\beta^{-}

Where x is the number of alpha particles and y is the number of beta particles.

Step-by-Step Calculation

1. **Calculate the number of alpha particles**:
   The decay involves the reduction of mass number from 238 to 206. Since each alpha particle reduces the mass number by 4, the number of alpha particles emitted is: \frac{238 - 206}{4} = 8.
2. **Calculate the number of beta particles**:
   The atomic number decreases from 92 to 82. However, it also increases due to beta decay (each beta decay increases the atomic number by 1). Therefore, because x alpha particles decrease the atomic number by 2x, and we have:
   92 - 2x + y = 82
   Substituting x = 8:
   92 - 2(8) + y = 82
   92 - 16 + y = 82
   y = 82 - 76
   y = 6.

Conclusion

In the decay of Uranium-238 to Lead-206, 8 alpha particles and 6 beta particles are emitted. Hence, the correct answer is: 8 alpha particles and 6 beta particles.