= Solution
The bracketed diagram energies are nuclear, so subtract one <electron> rest <energy> from each parent-to-daughter <energy> difference. The three kinetic-energy endpoints are
$$
Q_N=9.190-0.511=8.679\ \mathrm{MeV},\quad
Q_{Ne}=16.26-2.25-0.511=13.499\ \mathrm{MeV},\quad
Q_F=2.25-0.511=1.739\ \mathrm{MeV}.
$$
The observed partial-rate ratios are $\lambda_N/\lambda_{Ne}=0.19672$ and $\lambda_N/\lambda_F=0.24918$.
To obtain the simple Sargent-law estimates, define an effective strength by $\lambda=C|M_{\rm eff}|^2Q^5$, using the same normalization $C$. Then
$$
\boxed{\frac{|M_{\rm eff,N}|^2}{|M_{\rm eff,Ne}|^2}
\simeq0.19672\left(\frac{13.499}{8.679}\right)^5=1.79,}
$$
$$
\boxed{\frac{|M_{\rm eff,N}|^2}{|M_{\rm eff,F}|^2}
\simeq0.24918\left(\frac{1.739}{8.679}\right)^5
=8.05\times10^{-5}.}
$$
Thus the two forbidden branches have effective strengths of the same broad order, whereas the N ground-state branch is highly suppressed relative to the allowed F branch after this approximate fifth-power kinematic scaling. The first comparison involves mirror transitions with related nuclear configurations; order-of-magnitude similarity is reasonable, without expecting exact equality from this estimate.
These effective strengths must not be confused with precisely extracted microscopic reduced nuclear <matrix elements>. Both N and Ne ground-state branches are first-forbidden unique, for which the <first-forbidden unique beta-decay phase space> contains an additional factor proportional to $p_e^2+E_\nu^2$. In the massless, no-Coulomb limit this gives $Q^7$, so using the same microscopic unique-forbidden normalization for those two branches instead yields
$$
\boxed{\frac{|M_{U,N}|^2}{|M_{U,Ne}|^2}
\simeq0.19672\left(\frac{13.499}{8.679}\right)^7=4.33.}
$$
Comparing a unique-forbidden reduced operator directly with an allowed reduced operator also requires a convention for its powers of length and <momentum>. The number $8.05\times10^{-5}$ is consequently an effective Sargent-normalized suppression, not a universal dimensionless ratio between different operator ranks. Electron-mass and opposite-sign Coulomb corrections matter, particularly for the low-energy F branch. The data justify approximate strength comparisons; they do not fix precision nuclear <matrix elements> without these extra ingredients.
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