Question

The wavelength of \(\mathrm{x}\) rays is of the order of (A) \(1 \mathrm{~cm}\) (B) \(1 \mathrm{~m}\) (C) Imicron (D) 1angstrom

Short answer

The wavelength of x-rays is of the order of 1 angstrom, which falls within the x-ray wavelength range of \(10^{-9}\) m to \(10^{-12}\) m. Therefore, the correct answer is (D).

Step-by-step solution

1. Compare with standard x-ray wavelength range

First, we need to know the standard wavelength range of x-rays. The wavelength of x-rays typically falls within the range of \(10^{-9}\) m (nanometer) to \(10^{-12}\) m (picometer). We will compare each given option with this range to find the correct answer.

2. Convert units and compare

We will now convert each given option to meters so that we can compare them with the standard x-ray wavelength range. (A) \(1 \: cm = 1 \times 10^{-2} \: m\) (B) \(1 \: m\) (C) 1 micron (micrometer) = \(1 \times 10^{-6} \: m\) (D) 1 angstrom = \(1 \times 10^{-10} \: m\)

3. Choose the correct option

Now, let's compare each of these converted options with the standard x-ray wavelength range: (A) \(1 \times 10^{-2} \: m\) is far too large for an x-ray wavelength. (B) \(1 \: m\) is also too large for an x-ray wavelength. (C) \(1 \times 10^{-6} \: m\) is smaller than the range of x-ray wavelengths, but it is still larger than the usual x-ray wavelengths. (D) \(1 \times 10^{-10} \: m\) falls within the x-ray wavelength range, indicating that this is the correct answer. So, the wavelength of x-rays is of the order of 1 angstrom. The correct answer is (D).

Key concepts

Wavelength Units

When discussing the wavelengths of light waves, including x-rays, we have to express measurements in units that are both meaningful and precise. Common units for wavelength measure include meters (m), centimeters (cm), microns (micrometers), and angstroms. Each of these units serves a purpose, with meters being the SI unit of length, while smaller units like microns and angstroms are used to measure very short wavelengths.

To give it some context:

• 1 meter (m) is a common way to express larger distances.
• 1 centimeter (cm) is 0.01 meters (1 cm = 10^-2 m).
• 1 micron, also known as a micrometer, is 0.000001 meters (1 µm = 10^-6 m).
• 1 angstrom is 0.0000000001 meters (1 Å = 10^-10 m).

Each of these units is crucial for precise measurement, especially at microscopic and atomic scales, such as those of x-rays.

Standard X-ray Wavelength Range

X-rays possess high energy and relatively short wavelengths compared to visible light. The wavelength of x-rays falls within the distinctive range of 1 nanometer (nm) or 10^-9 meters to 0.001 nanometers or 10^-12 meters. This range is essential as it defines the area of the electromagnetic spectrum where x-rays reside.

Their short wavelengths are why x-rays can penetrate objects like human tissues or matter that visible light cannot. When x-ray beams pass through an object, they are either absorbed or scattered, which is how x-ray imaging in fields such as medicine works so effectively. Comparing given options with this range helps in determining if they're plausible for x-ray emissions.

Unit Conversion

Unit conversion is a vital process in science and engineering as it allows for a standardized comparison across different unit measures. Such conversions are essential when dealing with problems that involve various units.

For the problem of identifying x-ray wavelengths, the conversion of given options into meters helps to align them for direct comparison with the x-ray wavelength range. Here's how you convert:

• 1 cm converts to 10^-2 m.
• 1 m stays as 10⁰ m, although usually it's the base unit, so no conversion is needed.
• 1 micron (micrometer) is converted to 10^-6 m.
• 1 angstrom converts to 10^-10 m.

By converting each option to meters, it's easier to see which ones fall within the standard x-ray wavelength range, helping to arrive at the correct solution.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, including visible light, infrared, ultraviolet, and critical to this exercise, x-rays. Each type of radiation has a specific wavelength range, which impacts its energy level and its typical uses.

X-rays are part of this spectrum, situated between ultraviolet rays and gamma rays, characterized by their short wavelengths. The shorter the wavelength, the higher the energy; this is why x-rays are powerful and can penetrate most materials.

Understanding where x-rays fit on the electromagnetic spectrum helps us comprehend their applications in fields ranging from medical imaging, where they can visualize the interior of the human body, to crystallography, which studies the atomic structure of materials. It's important to recognize that the distinct properties of x-ray wavelengths lend themselves to these advanced applications.