An x-ray has a wavelength of \( 2.2 \times 10-11 \mathrm{~m} \). Whatis the freauency \( \begin{array}{l}1.4 \times 10^{19} \mathrm{~Hz} \\ 3.0 \times 10^{-23} \mathrm{~Hz} \\ 0.0066 \mathrm{~Hz} \\ 7.3 \times 10^{-20} \mathrm{~Hz}\end{array} \)

To find the frequency (\(f\)) of the x-ray, you can use the formula: \[ f = \frac{c}{\lambda} \] where \(c\) is the speed of light (\(3.0 \times 10^8 \mathrm{~m/s}\)) and \(\lambda\) is the wavelength (\(2.2 \times 10^{-11} \mathrm{~m}\)). Plugging in these values: \[ f = \frac{3.0 \times 10^8}{2.2 \times 10^{-11}} \approx 1.36 \times 10^{19} \mathrm{~Hz} \] This means the frequency of the x-ray is approximately \( 1.4 \times 10^{19} \mathrm{~Hz} \), rounding the last digits appropriately. X-rays play a crucial role in medical imaging, allowing doctors to see inside the human body without invasive procedures. Their high frequency and energy make them capable of penetrating soft tissues while being absorbed by denser materials such as bones, providing clear images for diagnosis. Just imagine, with this technology, physicians can pinpoint issues like fractures or tumors without surgery—how cool is that? Understanding the properties of x-rays is not just fascinating but also essential for safety in medical and industrial applications. Overexposure can lead to harmful effects due to their ionizing nature; hence protocols are in place to minimize exposure to both patients and medical personnel. It’s amazing to see how science balances effective diagnostics with health precautions!