Question

Wavelength of X-rays having the largest penetrating power is:

• A. \(1.2 \, \text{\AA}\)
• B. \(6 \, \text{\AA}\)
• C. \(9 \, \text{\AA}\)
• D. \(12 \, \text{\AA}\)

Hint:

This is a fundamental concept in electromagnetic radiation: Short Wavelength \(\leftrightarrow\) High Frequency \(\leftrightarrow\) High Energy \(\leftrightarrow\) High Penetrating Power. This applies to the entire EM spectrum, from radio waves to gamma rays.

Answer 1

The Correct Option is A

Step 1: Relate penetrating power to the energy of a photon. The penetrating power of electromagnetic radiation, like X-rays, is directly proportional to the energy of its photons. Higher energy photons are more penetrating.
Step 2: Recall the energy-wavelength relationship for a photon. The energy (\(E\)) of a photon is inversely proportional to its wavelength (\(\lambda\)): \[ E = hf = \frac{hc}{\lambda} \] where \(h\) is Planck's constant and \(c\) is the speed of light.
Step 3: Determine which wavelength corresponds to the highest energy. To have the largest penetrating power, the X-ray must have the highest energy. According to the formula, the highest energy corresponds to the shortest (smallest) wavelength.
Step 4: Compare the given wavelengths. The given 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 have the highest energy and therefore the largest penetrating power.