The isotope `._92U^238` decays successively to form `._90Th^234 , ._91Pa^234 , ._92U^234 , ._90Th^230` and `._88Ra^226`. What are the radiations emitted in these five steps?

Options

A. `alpha,alpha,alpha,beta,beta`
B. `alpha,beta,beta,alpha,beta`
C. `alpha,beta,alpha,alpha,alpha`
D. `alpha,beta,beta,alpha,alpha`

Answer

To determine the types of radiation emitted during the decay of the isotope \( _{92}^{238}\text{U} \) to form \( _{90}^{234}\text{Th} \), \( _{91}^{234}\text{Pa} \), \( _{92}^{234}\text{U} \), \( _{90}^{230}\text{Th} \), and \( _{88}^{226}\text{Ra} \), we can analyze each step of the decay process based on the changes in atomic number and mass number.

### Step-by-Step Solution:

1. **Decay of \( _{92}^{238}\text{U} \) to \( _{90}^{234}\text{Th} \)**:
- The atomic number decreases from 92 to 90 (a decrease of 2).
- The mass number decreases from 238 to 234 (a decrease of 4).
- This indicates the emission of an **alpha particle** (which consists of 2 protons and 2 neutrons).
- **Radiation emitted**: Alpha radiation.

2. **Decay of \( _{90}^{234}\text{Th} \) to \( _{91}^{234}\text{Pa} \)**:
- The atomic number increases from 90 to 91 (an increase of 1).
- The mass number remains the same at 234.
- This indicates the emission of a **beta particle** (which is a high-energy electron).
- **Radiation emitted**: Beta radiation.

3. **Decay of \( _{91}^{234}\text{Pa} \) to \( _{92}^{234}\text{U} \)**:
- The atomic number increases from 91 to 92 (an increase of 1).
- The mass number remains the same at 234.
- This indicates the emission of another **beta particle**.
- **Radiation emitted**: Beta radiation.

4. **Decay of \( _{92}^{234}\text{U} \) to \( _{90}^{230}\text{Th} \)**:
- The atomic number decreases from 92 to 90 (a decrease of 2).
- The mass number decreases from 234 to 230 (a decrease of 4).
- This indicates the emission of an **alpha particle**.
- **Radiation emitted**: Alpha radiation.

5. **Decay of \( _{90}^{230}\text{Th} \) to \( _{88}^{226}\text{Ra} \)**:
- The atomic number decreases from 90 to 88 (a decrease of 2).
- The mass number decreases from 230 to 226 (a decrease of 4).
- This indicates the emission of another **alpha particle**.
- **Radiation emitted**: Alpha radiation.

### Summary of Radiations Emitted:
- Step 1: Alpha radiation
- Step 2: Beta radiation
- Step 3: Beta radiation
- Step 4: Alpha radiation
- Step 5: Alpha radiation

### Final Answer:
The sequence of radiations emitted is: **Alpha, Beta, Beta, Alpha, Alpha**.

---