X-ray Radiation Wavelength Identification

The question asks to identify which given wavelength of radiation might correspond to an X-ray. To answer this, we need to understand the electromagnetic spectrum and the typical wavelength ranges associated with different types of radiation, particularly X-rays.

Understanding the Electromagnetic Spectrum

The electromagnetic spectrum is the range of all possible frequencies (or wavelengths) of electromagnetic radiation. The spectrum includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. These are all fundamentally the same phenomenon but differ in their wavelength and frequency, and consequently, their energy.

Wavelength (\(\lambda\)) and frequency (\(\nu\)) are inversely related by the speed of light (\(c\)): \(\lambda = c/\nu\). Energy (\(E\)) is directly proportional to frequency: \(E = h\nu\), where \(h\) is Planck's constant. Therefore, shorter wavelengths correspond to higher frequencies and higher energies.

Typical Wavelength Ranges

Here are the approximate wavelength ranges for relevant parts of the electromagnetic spectrum:

• Gamma Rays: Less than 0.01 nanometers (\(< 0.01 \text{ nm}\)).
• X-rays: Generally considered to be in the range of 0.01 nm to 10 nm. This range is often divided into hard X-rays (shorter wavelengths, higher energy) and soft X-rays (longer wavelengths, lower energy).
• Ultraviolet (UV) Radiation: Roughly 10 nm to 400 nm.
• Visible Light: Approximately 400 nm to 700 nm.

Analyzing the Options for X-ray Radiation

Let's examine each option provided in the question:

• Option 1: \(1 \text{ nm}\)

  A wavelength of 1 nanometer falls within the range typically defined for X-rays (0.01 nm to 10 nm). Specifically, it represents a soft X-ray.

• Option 2: \(10 \text{ nm}\)

  A wavelength of 10 nanometers is at the upper boundary of the X-ray range and the lower boundary of the ultraviolet range. It can sometimes be classified as a very soft X-ray or extreme ultraviolet (EUV) radiation.

• Option 3: \(100 \text{ nm}\)

  A wavelength of 100 nanometers falls squarely within the ultraviolet (UV) portion of the electromagnetic spectrum, not X-rays.

• Option 4: \(300 \text{ nm}\)

  A wavelength of 300 nanometers is also well within the ultraviolet (UV) range, closer to the visible light spectrum.

Conclusion on X-ray Wavelength

Based on the standard classification of the electromagnetic spectrum, X-rays have wavelengths ranging from approximately 0.01 nm to 10 nm. Among the given options, 1 nm clearly falls within this defined range for X-ray radiation.