Which of the following is the radio isotope in each pair (a) (b) and (c ) ?
(a) ` ""_(6)^(12) C, _(6)^(14) C` (b) ` ""_(15)^(30) P, _(15)^(32) P` (c ) ` ""_(19)^(39) K, _(19)^(40) K`
Give reason for your answer.

Answer

To determine the radioactive isotope in each pair, we need to analyze the isotopes based on their neutron count. Isotopes are variants of the same chemical element that have the same number of protons but different numbers of neutrons. Generally, isotopes with a higher neutron count tend to be more unstable and therefore more radioactive.

### Step-by-Step Solution:

1. **Identify the Isotopes and Their Neutron Counts:**
- For (a) Carbon isotopes:
- \( _{6}^{12}C \): Number of neutrons = 12 - 6 = 6
- \( _{6}^{14}C \): Number of neutrons = 14 - 6 = 8
- For (b) Phosphorus isotopes:
- \( _{15}^{30}P \): Number of neutrons = 30 - 15 = 15
- \( _{15}^{32}P \): Number of neutrons = 32 - 15 = 17
- For (c) Potassium isotopes:
- \( _{19}^{39}K \): Number of neutrons = 39 - 19 = 20
- \( _{19}^{40}K \): Number of neutrons = 40 - 19 = 21

2. **Compare the Neutron Counts:**
- For Carbon:
- \( _{6}^{12}C \) has 6 neutrons.
- \( _{6}^{14}C \) has 8 neutrons.
- **Conclusion:** \( _{6}^{14}C \) is the radioactive isotope because it has more neutrons.

- For Phosphorus:
- \( _{15}^{30}P \) has 15 neutrons.
- \( _{15}^{32}P \) has 17 neutrons.
- **Conclusion:** \( _{15}^{32}P \) is the radioactive isotope because it has more neutrons.

- For Potassium:
- \( _{19}^{39}K \) has 20 neutrons.
- \( _{19}^{40}K \) has 21 neutrons.
- **Conclusion:** \( _{19}^{40}K \) is the radioactive isotope because it has more neutrons.

3. **Final Answers:**
- (a) \( _{6}^{14}C \)
- (b) \( _{15}^{32}P \)
- (c) \( _{19}^{40}K \)