On comparing chemical reactivity of `C^12 and C^14` , it is revealed that:

Options

A. `C^12` is more reactive
B. `C^14` is more reactive
C. Both are inactive
D. Both are equally active

Answer

To compare the chemical reactivity of the isotopes \( C^{12} \) and \( C^{14} \), we can follow these steps:

### Step 1: Identify the Isotopes
Both \( C^{12} \) and \( C^{14} \) are isotopes of carbon. They have the same atomic number, which is 6 (indicating they are both carbon), but different mass numbers: 12 and 14, respectively.

### Step 2: Determine the Number of Protons and Neutrons
- For \( C^{12} \):
- Number of protons = Atomic number = 6
- Mass number = Number of protons + Number of neutrons
- Therefore, \( 12 = 6 + \text{Number of neutrons} \)
- Number of neutrons = \( 12 - 6 = 6 \)

- For \( C^{14} \):
- Number of protons = Atomic number = 6
- Mass number = Number of protons + Number of neutrons
- Therefore, \( 14 = 6 + \text{Number of neutrons} \)
- Number of neutrons = \( 14 - 6 = 8 \)

### Step 3: Calculate the Neutron to Proton Ratio
- For \( C^{12} \):
- Neutron to proton ratio = \( \frac{6}{6} = 1 \)

- For \( C^{14} \):
- Neutron to proton ratio = \( \frac{8}{6} = \frac{4}{3} \)

### Step 4: Analyze Stability
- A neutron to proton ratio of 1 (for \( C^{12} \)) indicates stability.
- A neutron to proton ratio greater than 1 (for \( C^{14} \)) indicates instability.

### Step 5: Conclusion on Reactivity
- \( C^{12} \) is stable and will not react much as it does not need to gain stability.
- \( C^{14} \) is unstable and will be more reactive as it seeks to gain stability.

Thus, we conclude that \( C^{14} \) is more reactive than \( C^{12} \).

### Final Answer
The correct conclusion is that \( C^{14} \) is more reactive than \( C^{12} \).

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