Calculate the neutron-proton ratios for the following nuclides, and determine where they lie in relation to the band of stability. a. 235 /92 U b. 16/8 O c. 56/26 Fe d. 156/60 Nd
Answer
⚛️ Neutron-Proton Ratio & Band of Stability Analysis
🔍 Step-by-Step Method
To analyze the neutron-proton ratio (n/p), we:
- Subtract atomic number (Z) from mass number (A) to get the number of neutrons (N)
- Compute the ratio: n/p = N / Z
- Compare the ratio to the band of stability:
- For light elements (Z ≤ 20), stable n/p ≈ 1
- For heavier elements, stable n/p ≈ 1.3–1.5
🧪 Nuclide Calculations
🔹 a. 235U (Z = 92)
Neutrons = 235 − 92 = 143
n/p = 143 / 92 ≈ 1.55
🔎 This ratio is slightly **above the band of stability**, indicating it may be radioactive and decay to reach a more stable configuration.
n/p = 143 / 92 ≈ 1.55
🔎 This ratio is slightly **above the band of stability**, indicating it may be radioactive and decay to reach a more stable configuration.
🔹 b. 16O (Z = 8)
Neutrons = 16 − 8 = 8
n/p = 8 / 8 = 1.00
✅ This lies **on the band of stability**, meaning 16O is stable.
n/p = 8 / 8 = 1.00
✅ This lies **on the band of stability**, meaning 16O is stable.
🔹 c. 56Fe (Z = 26)
Neutrons = 56 − 26 = 30
n/p = 30 / 26 ≈ 1.15
✅ This is **within the band of stability**, as iron-56 is a well-known stable isotope.
n/p = 30 / 26 ≈ 1.15
✅ This is **within the band of stability**, as iron-56 is a well-known stable isotope.
🔹 d. 156Nd (Z = 60)
Neutrons = 156 − 60 = 96
n/p = 96 / 60 = 1.60
⚠️ This is **above the stable band**, suggesting possible beta decay (neutron → proton) to reach stability.
n/p = 96 / 60 = 1.60
⚠️ This is **above the stable band**, suggesting possible beta decay (neutron → proton) to reach stability.
📊 Summary Table
| Nuclide | Neutrons | Protons (Z) | n/p Ratio | Band of Stability |
|---|---|---|---|---|
| 235U | 143 | 92 | 1.55 | Above |
| 16O | 8 | 8 | 1.00 | Stable |
| 56Fe | 30 | 26 | 1.15 | Stable |
| 156Nd | 96 | 60 | 1.60 | Above |
📌 Final Insight
Stable nuclei tend to have n/p ratios close to 1 (light elements) or 1.3–1.5 (heavier elements). Ratios significantly above the band of stability often lead to radioactive decay until the nucleus becomes more stable.