= Solution
Using the observed counts,
$$
N_1+N_4+N_6=1\,275\,240,\qquad
1-\Gamma_0=0.33.
$$
Thus
$$
\boxed{\begin{aligned}
\Gamma_1&=0.33\frac{1\,230\,470}{1\,275\,240}=0.318415\simeq31.84\%,\\
\Gamma_2&=0.33\frac{42\,269}{1\,275\,240}=0.0109382\simeq1.094\%,\\
\Gamma_3&=0.33\frac{2501}{1\,275\,240}=0.000647196\simeq0.06472\%.
\end{aligned}}
$$
Together with the $67\%$ direct <ground state> branch, these sum to unity. No measurement uncertainties were supplied for these ratios, so the extra digits only document the arithmetic.
Back to article page
