Step 1: Establish the connection between photon energy and penetrating power. The penetrating capability of electromagnetic radiation, such as X-rays, is directly proportional to the energy of its constituent photons. Photons with higher energy exhibit greater penetration.
Step 2: State the energy-wavelength relationship for a photon. The energy (\(E\)) of a photon is inversely proportional to its wavelength (\(\lambda\)):
\[
E = hf = \frac{hc}{\lambda}
\]
Here, \(h\) represents Planck's constant, and \(c\) denotes the speed of light.
Step 3: Identify the wavelength associated with maximum energy. For maximal penetrating power, the X-ray must possess the highest energy. Based on the given formula, the highest energy is associated with the shortest (smallest) wavelength.
Step 4: Compare the provided wavelengths. The available options are \(1.2 \, \text{\AA}\), \(6 \, \text{\AA}\), \(9 \, \text{\AA}\), and \(12 \, \text{\AA}\). The smallest value among these is \(1.2 \, \text{\AA}\). This wavelength will correspond to the highest energy and consequently the greatest penetrating power.