`C^(14)` is radioactive. The activity and the disintegration product are

Options

A. `beta-`active, `._(7)N^(14)`
B. `alpha - " active, " ._(7)Be^(10)`
C. Positron active, `._(5)B^(14)`
D. `gamma-"active ", C^(14)`

Explanation

To solve the question regarding the radioactive isotope Carbon-14, we need to determine its activity and the disintegration product. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding Carbon-14
Carbon-14 (\(^{14}C\)) is a radioactive isotope of carbon. It is formed in the atmosphere when nitrogen-14 (\(^{14}N\)) is bombarded by cosmic rays.

**Hint:** Remember that isotopes have the same number of protons but different numbers of neutrons.

### Step 2: Identifying the Type of Decay
Carbon-14 undergoes beta decay. In this process, a neutron in the carbon-14 nucleus is converted into a proton, which results in the emission of a beta particle (an electron).

**Hint:** Beta decay involves the transformation of a neutron into a proton, which increases the atomic number by 1.

### Step 3: Writing the Decay Equation
The decay of Carbon-14 can be represented by the following nuclear reaction:
\[ ^{14}_{6}C \rightarrow ^{14}_{7}N + \beta^- \]
Where:
- \(^{14}_{6}C\) is Carbon-14,
- \(^{14}_{7}N\) is Nitrogen-14 (the disintegration product),
- \(\beta^-\) represents the emitted beta particle.

**Hint:** In a nuclear reaction, the sum of the atomic numbers and mass numbers must be conserved.

### Step 4: Identifying the Activity
The activity of a radioactive substance refers to the rate at which it decays, which is typically measured in disintegrations per second. For Carbon-14, its activity is due to its beta decay.

**Hint:** The activity can be quantified using the decay constant and the number of radioactive nuclei present.

### Conclusion
Thus, the activity of Carbon-14 is due to its beta decay, and the disintegration product is Nitrogen-14.

**Final Answer:**
- **Activity:** Beta active
- **Disintegration Product:** Nitrogen-14 (\(^{14}N\))