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X-rays are a form of electromagnetic radiation, just like visible light, but with much shorter wavelengths. Understanding their wavelength is vital for various applications, from medical imaging to studying the structure of crystals.

• The wavelength of x-rays typically ranges between 0.01 to 10 nanometers, often measured in picometers (pm) when they are very short, like in this exercise.
• In scientific notations, x-ray wavelengths are generally expressed in meters, converting from picometers by multiplying by 10^-12.

For the problem at hand, the given x-ray wavelength is 35 pm. This means it is highly energetic as shorter wavelengths correspond to higher energy levels. This fundamental property is why x-rays can penetrate substances and are useful in imaging technologies and detailed material investigations.

The frequency of an electromagnetic wave is a measure of how many wave cycles pass a given point per second. This can be computed from the wavelength using the simple relationship:\[ u = \frac{c}{\lambda} \]Here, \( c \) is the speed of light, approximately \(3.00 \times 10^8 \mathrm{m/s}\), and \( \lambda \) is the wavelength. This equation highlights the inverse relationship between the wavelength and frequency, meaning the shorter the wavelength, the higher the frequency.In the exercise, the x-ray's wavelength of 35 pm was converted to meters, and then used to calculate the frequency: \[ u = \frac{3.00 \times 10^8}{35.0 \times 10^{-12}} \approx 8.57 \times 10^{18} \mathrm{Hz} \]This calculation results in x-rays having a very high frequency, which correlates to their ability to carry significant amounts of energy.

Photon momentum might initially seem paradoxical, as photons are massless. However, they do possess momentum as they travel at the speed of light. The momentum of a photon is computed using the relationship:\[ p = \frac{E}{c} \]Where \( E \) is the energy of the photon and \( c \) is the speed of light. Typically, photon energy is first calculated with Planck's formula, \( E = hu \), before calculating momentum. In the given problem, after finding the photon energy, momentum was calculated as: \[ p = \frac{5.68 \times 10^{-15}}{3.00 \times 10^8} \approx 1.89 \times 10^{-23} \mathrm{kg \cdot m/s} \]Moreover, it's common to express photon momentum in units of \( \mathrm{eV}/c \) or \( \mathrm{keV}/c \), underscoring its energy-like nature. In simpler terms, photon momentum helps explain phenomena such as radiation pressure, which is how light can exert force on objects.