Final answer:
X-rays have significantly shorter wavelengths and higher frequencies compared to visible light, which results in X-rays having greater energy and the ability to penetrate matter more deeply.
Step-by-step explanation:
The statement that X-rays are similar to visible light but with much shorter wavelengths and greater energy is indeed true. Comparing the properties of X-rays and visible light, we can confirm that X-rays have shorter wavelengths ranging from 0.01 nanometers to 20 nanometers, and consequently, they also have higher frequencies than visible light. This means that the option stating that X-rays have higher frequencies and shorter wavelengths than visible light, which allows them to penetrate matter more deeply, is correct.
Specifically, this corresponds to option d from the provided choices, which correctly states that X-rays have wavelengths between 1 × 10−8 – 5 × 10−12 meters and frequencies between 3 × 1016 - 6 × 1019 Hz, which is significantly more compared to visible light's wavelength and frequency range of 7.5 × 10−7 – 4.0 × 10−7 meters and 4.0 × 1014 – 7.5 x 1014 Hz respectively.