Thermal (slow) neutrons at 0.025 eV: estimate the typical speed of such neutrons in metres per second for reactor physics calculations.

Introduction / Context:In thermal reactors, neutron speeds at room temperature are often approximated for quick calculations and intuition. A widely used reference energy is 0.025 eV, corresponding to standard “thermal” conditions near 20–25 °C.

Given Data / Assumptions:

• Neutron kinetic energy E ≈ 0.025 eV representative of room-temperature thermal neutrons.
• We need an order-of-magnitude speed used in hand calculations.
• Non-relativistic kinetic energy relation applies.

Concept / Approach:For non-relativistic particles, E = (1/2) * m * v^2. Using E ≈ 0.025 eV and neutron mass m_n, the commonly memorized result is v ≈ 2200 m/s (more precisely ~2200 m/s at 20 °C). This becomes a standard constant used in cross-section-to-reaction-rate conversions at “2200 m/s” reference conditions in many nuclear data libraries.

Step-by-Step Solution:Recall thermal reference: E_ref ≈ 0.025 eV.Use the standard tabulated equivalence: E_ref ↔ v ≈ 2200 m/s.Select 2200 as the typical value.

Verification / Alternative check:Detailed calculation with constants (converting eV to joules and inserting neutron mass) yields a velocity close to 2.2 * 10^3 m/s, confirming the memorized figure.

Why Other Options Are Wrong:

• 1100, 3300, 4400, 1500: Not the standard reference velocity for 0.025 eV; 2200 m/s is the accepted benchmark.

Common Pitfalls:Forgetting that “thermal” is a temperature-dependent distribution; 2200 m/s is a convenient reference, not a unique speed for all thermal neutrons.

Final Answer:2200