NUC-04

Reaction Q-value

Q = (m_i − m_f) c². Exothermic if Q > 0.

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NuclearQ-value

Governing equation

Q=(m_i-m_f)c^2

$m_f \in \left[1, 240\right]$

where

m_i: Initial mass (u)
m_f: Final mass (u)
Q: Q-value (MeV)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

Q=(m_i-m_f)c^2

$m_f \in \left[1, 240\right]$

$m_f = 1$ $Q = 2824.3$

Along the curve

②

Domain of the variable — blue

m_f_{\min} = 1,\quad m_f_{\max} = 240

$m_f \in \left[1, 240\right]$

$m_f = 1$ $m_f = 1$

Along the curve

③

Response curve — green

Q=(m_i-m_f)c^2

$m_f \in \left[1, 240\right]$

$m_f = 1$ $Q = 2824.3$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q}{\mathrm{d}m_f}

$m_f \in \left[1, 240\right]$

$m_f = 2.503$ $Q^{\prime} = -931.5$

Along the curve

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-04 — Reaction Q-value) is the form associated with Q-value. Working symbols: $m_i$ , $m_f$ $\rightarrow$ $Q$ . Masses in atomic mass units, 931.494 MeV/u. The kinetic energy released in the CM frame.

Purpose

Purpose: compute

Q

from

m_i

m_f

in Nuclear physics via

Q=(m_i-m_f)c^2

Q = (m_i − m_f) c². Exothermic if Q > 0. 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_i = 4.032\,\mathrm{u}

m_f = 4.002\,\mathrm{u}

, the governing relation

Q=(m_i-m_f)c^2

yields

Q = 28.411\,\mathrm{MeV}

. Two mass bars, a Q arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Initial mass m_i4.032 uFinal mass m_f4.0015 u

Outputs

Q-value Q28.411 MeV

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Narration of this film

Two mass bars, a Q arrow.

Masses in atomic mass units, 931.494 MeV/u. The kinetic energy released in the CM frame.

Reading speed

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