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Bethe–Feynman formula

The Bethe–Feynman formula is a historical theoretical relation for estimating the efficiency and energy yield of a fission explosive from bulk physical parameters.

Version
v1 · 2026-09-28 · History
Domain-specific #
8169
Domain group
Natural Sciences
Origin domain
Physics
Subdomains
Nuclear Physics, Nuclear Weapons Physics → Physics

Core Idea

Bethe–Feynman formula is treated here as the recurring naturalsciencesengineeringhealth identity summarized by this source-grounded definition: The Bethe–Feynman formula is a historical theoretical relation for estimating the efficiency and energy yield of a fission explosive from bulk physical parameters. The Bethe–Feynman efficiency formula, a simple method for calculating the yield of a fission bomb, was first derived in 1943 after development in 1942. The Bethe–Feynman formula is a historical theoretical relation for estimating the efficiency and energy yield of a fission explosive from bulk physical parameters. where γ is the thermodynamic exponent.

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The Old Quick-Guess Rule

Long ago, scientists came up with a shortcut math rule. It let them guess, using a few big measurements, how much energy a certain kind of very powerful bomb would release. That shortcut is called the Bethe–Feynman formula.

Early Bomb Yield Estimate

The Bethe–Feynman formula is a historical science formula from the 1940s. It gave a simple way to estimate how efficient a fission explosive would be, meaning how much of its fuel would actually release energy, and so how big the yield would be. Rather than simulating everything, it used a few overall properties, like how fast the reaction grows and how far the material is beyond the size needed to keep the reaction going. Some parts of it are thought to still be kept secret.

Historical Fission Yield Formula

The Bethe–Feynman formula is a historical theoretical relation, first derived in 1943, for estimating the efficiency and energy yield of a fission explosive from a handful of bulk physical parameters. It combines quantities such as the fuel's prompt energy density, a thermodynamic exponent, a rate factor comparing neutron speed to reaction mean free path, the critical radius, and how far the assembly exceeds that critical radius. A numerical coefficient was included to improve its accuracy considerably. Its value lies in being a compact order-of-magnitude estimate rather than a detailed simulation. Aspects of it are speculated to remain restricted data, so the published form is not necessarily complete.

 

The Bethe–Feynman formula is a historical closed-form estimate, developed in 1942 and first derived in 1943, for the efficiency and yield of a fission explosive from bulk parameters rather than detailed simulation. As stated in the source, it is written in terms of the thermodynamic exponent γ of a photon gas, the prompt energy density of the fuel, α (neutron velocity divided by the total reaction mean free path, taken at its maximum), the critical radius R, and the excess supercritical radius δ, with an added numerical coefficient that improved accuracy by more than an order of magnitude. Its form is E_ff = (E₂/(γ−1)) · α_max² · R_crit² · (δ/(1−δ)) · ((2+3δ)/2). The abstraction is narrow: it is this specific efficiency relation, not fission physics generally, and aspects of it are speculated to be restricted data.

Scope of Application

  • Documented setting. The Bethe–Feynman efficiency formula, a simple method for calculating the yield of a fission bomb, was first derived in 1943 after development in 1942.

  • Related formula. A numerical coefficient would then be included to create the Bethe–Feynman formula—increasing accuracy by more than an order of magnitude.

  • Related formula. Eff = \left( \frac{E2}{\gamma-1} \right) \cdot \alpha{max}^2 \cdot R{crit}^2 \cdot \left(\frac{\delta}{1-\delta}\right) \cdot \left(\frac{2 + 3\delta}{2} \right).

  • Related formula. where γ is the thermodynamic exponent of a photon gas, is the prompt energy density of the fuel, α is V (neutron velocity) / λ (total reaction mean free path), R is.

  • Documented setting. The Bethe–Feynman formula is a historical theoretical relation for estimating the efficiency and energy yield of a fission explosive from bulk physical parameters.

Clarity

A clear use of Bethe–Feynman formula names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The Bethe–Feynman formula is a historical theoretical relation for estimating the efficiency and energy yield of a fission explosive from bulk physical parameters.

Manages Complexity

Bethe–Feynman formula compresses multiple naturalsciencesengineeringhealth details into a stable diagnostic relation. The source shows both the central mechanism—eff = \left( \frac{E2}{\gamma-1} \right) \cdot \alpha{max}^2 \cdot R{crit}^2 \cdot \left(\frac{\delta}{1-\delta}\right) \cdot \left(\frac{2 + 3\delta}{2} \right).—and the practical consequence—a numerical coefficient would then be included to create the Bethe–Feynman formula—increasing accuracy by more than.

Abstract Reasoning

  1. Type the carrier. Identify the naturalsciencesengineeringhealth entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: The Bethe–Feynman formula is a historical theoretical relation for estimating the efficiency and energy yield of a fission explosive from bulk physical parameters.
  3. Check operation and conditions. where γ is the thermodynamic exponent of a photon gas, is the prompt energy density of the fuel, α is V (neutron velocity) / λ (total reaction mean free path), R is the critical radius and 𝛿 is the.

Knowledge Transfer

Within the home domain. Knowledge about Bethe–Feynman formula transfers literally when a new case preserves the same carrier type, relation, and recognition test. The Bethe–Feynman efficiency formula, a simple method for calculating the yield of a fission bomb, was first derived in 1943 after development in 1942. A numerical coefficient would then be included to create the Bethe–Feynman formula—increasing accuracy by more than an order of magnitude. Beyond the home domain. No.

Neighborhood in Abstraction Space

Bethe–Feynman formula sits in a moderately populated region (41st percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Physical Quantities, Operators & Formulas (33 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08