In which of the following decays the atomic number decreases?
(i) `alpha`-decay (ii) `beta^(+)`-decay
(iii) `beta^(-)`-decay (iv) electron capture

Options

A. `(i),(ii),(iii)`
B. `(ii),(iii),(iv)`
C. `(i),(ii),(iv)`
D. all

Answer

To determine which of the given decays results in a decrease in atomic number, we will analyze each decay process step by step.

### Step 1: Analyze Alpha Decay
- In alpha decay, an alpha particle (which consists of 2 protons and 2 neutrons) is emitted from the nucleus.
- The atomic number (Z) of the original nucleus decreases by 2 because it loses 2 protons.
- The mass number (A) decreases by 4 because it loses 2 protons and 2 neutrons.
- **Conclusion**: The atomic number decreases by 2.

### Step 2: Analyze Beta Positive Decay
- In beta positive decay (β+ decay), a positron is emitted, which is the antiparticle of an electron.
- A proton in the nucleus is transformed into a neutron, resulting in a decrease of 1 in the atomic number.
- The mass number remains unchanged because the total number of nucleons (protons + neutrons) remains the same.
- **Conclusion**: The atomic number decreases by 1.

### Step 3: Analyze Beta Negative Decay
- In beta negative decay (β- decay), a neutron in the nucleus is transformed into a proton and an electron (beta particle) is emitted.
- The atomic number increases by 1 because a neutron is converted into a proton.
- The mass number remains unchanged.
- **Conclusion**: The atomic number increases by 1.

### Step 4: Analyze Electron Capture
- In electron capture, an electron from the surrounding environment is captured by the nucleus.
- This process converts a proton into a neutron, resulting in a decrease of 1 in the atomic number.
- The mass number remains unchanged.
- **Conclusion**: The atomic number decreases by 1.

### Final Conclusion
Based on the analysis:
- **Alpha decay**: Atomic number decreases by 2.
- **Beta positive decay**: Atomic number decreases by 1.
- **Beta negative decay**: Atomic number increases by 1.
- **Electron capture**: Atomic number decreases by 1.

Thus, the decays in which the atomic number decreases are:
- Alpha decay (i)
- Beta positive decay (ii)
- Electron capture (iv)

### Correct Answer
The correct options are (i), (ii), and (iv).

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