The x-ray has a frequency of \( 1.4 \times 10^{19} \mathrm{~Hz} \). What is the energy associated with one x-ray? \( 9.7 \times 10^{-33} \mathrm{~J} \) \( 9.3 \times 10^{-15} \mathrm{~J} \) \( 2.1 \times 10^{523} \mathrm{~J} \) \( 2.1 \times 10^{-11} \mathrm{~J} \)

To find the energy associated with one x-ray, we can use the formula \( E = h \cdot f \), where \( E \) is the energy, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)), and \( f \) is the frequency. Plugging in the values, we get \( E = (6.626 \times 10^{-34}) \cdot (1.4 \times 10^{19}) \), which calculates to approximately \( 9.3 \times 10^{-15} \, \text{J} \). In practical terms, x-rays are widely used in medical imaging to visualize the internal structures of the body. They help in diagnosing fractures, infections, and tumors. Beyond healthcare, x-rays are used in industries for non-destructive testing, ensuring the integrity of materials and components without damaging them. It's fascinating how a form of radiation helps keep us safe in so many aspects!