For copper,
\(v_{boom\,Cu}=3.4354*\cfrac{8960}{29}=1061.42\,ms^{-1}\)
For Hydrogen \(H_2\),
\(v_{boom\,H_2}=3.4354*\cfrac{0.08988}{1*2}=0.154\,ms^{-1}\)
If \(\Delta t=\cfrac{v}{c}-1\) and
\(\cfrac{S_{p\,Cu}}{S_{p\,H_2}}=\cfrac{\cfrac{v_{boom\,Cu}}{c}-1}{\cfrac{v_{boom\,H_2}}{c}-1}\)
where \(S_{p\,Cu}\) is the penetrating depth due X rays from copper...
\(S_{p\,H_2}=S_{p\,Cu}*\cfrac{\cfrac{v_{boom\,H_2}}{c}-1}{\cfrac{v_{boom\,Cu}}{c}-1}\)
We estimate \(S_{p\,Cu}\approx 20\,cm\),
\(S_{p\,H_2}=0.2*\cfrac{\cfrac{0.154}{299792458}-1}{\cfrac{1061.42}{299792458}-1}\)
\(S_{p\,H_2}==0.2000007\)
X ray due to \(H_2\) at \(v_{boom}\) is only slightly more penetrating than X ray due to \(Cu\) at \(v_{boom}\). An increase in value for \(S_p\) because the term,
\(\left|\cfrac{v_{boom\,H_2}}{c}-1\right|\gt\left|\cfrac{v_{boom\,Cu}}{c}-1\right|\)
since,
\(v_{boom\,H_2}\lt v _{boom\,Cu}\lt c\)
but the high value of \(c\) makes the increment insignificant.
It is best to measure \(S_{p}\) directly. In the setup below,
\(S_p\) is varied as the detector, at a fixed distance \(D\) from the metal plates with surface features sandwiched in the middle, detects a clear image of the interior of the plates. If X ray penetration is due to a spread of torus photons around \(v_{boom}\), the detector will see the hidden surface features in the metal plates, over a range of values \(S_{p}\). Increasing the detector distance \(D\) narrows this range. The plates are sufficiently thin to allow the interior features to be detected by X ray.
Then,
\(S_p=\cfrac{S_{p\,1}+S_{p\,2}}{2}\)
A series of \(D\) values would narrows the variance in \(S_{p}\).
Maybe then the expression,
\(\Delta t=\cfrac{v}{c}-1\)
\(v=v_{boom}\)
can be verified, after quantifying Earth's movement.
