NUC-06

Fusion Q-value

Q = (m_a + m_b − m_c − m_d) × 931.494 MeV. Two-body fusion to two products.

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NuclearFusion Q

Governing equation

Q=(m_a+m_b-m_c-m_d)\,931.494\,\mathrm{MeV}

where

m_a: Mass a (u)
m_b: Mass b (u)
m_c: Mass c (u)
m_d: Mass d (u)
Q: Fusion Q (MeV)

Lecture brief

Historical brief

Rutherford, Chadwick, the semi-empirical mass formula, fission (Hahn–Strassmann 1938) and fusion Q-values, then Compton and Bethe–Bloch stopping, are the nuclear toolkit. Decay, binding and dose start here. This sheet (NUC-06 — Fusion Q-value) is the form associated with Fusion Q. Working symbols: $m_a$ , $m_b$ , $m_c$ , $m_d$ $\rightarrow$ $Q$ . DT: 17.6 MeV. The Sun burns pp-chain at a much smaller Q per nucleon, slowly.

Purpose

Purpose: compute

Q

from

m_a

m_b

m_c

m_d

in Nuclear physics via

Q=(m_a+m_b-m_c-m_d)\,931.494\,\mathrm{MeV}

Q = (m_a + m_b − m_c − m_d) × 931.494 MeV. Two-body fusion to two products. Use it when a real nuclear physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

m_a = 2.014\,\mathrm{u}

m_b = 3.016\,\mathrm{u}

m_c = 4.003\,\mathrm{u}

m_d = 1.009\,\mathrm{u}

, the governing relation

Q=(m_a+m_b-m_c-m_d)\,931.494\,\mathrm{MeV}

yields

Q = 17.512\,\mathrm{MeV}

. Two light nuclei, a heavier product, a Q flash. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass a m_a2.0141 uMass b m_b3.016 uMass c m_c4.0026 uMass d m_d1.0087 u

Outputs

Fusion Q Q17.512 MeV

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Narration of this film

Two light nuclei, a heavier product, a Q flash.

DT: 17.6 MeV. The Sun burns pp-chain at a much smaller Q per nucleon, slowly.

Reading speed

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