Question

The wavelength of \(\mathrm{x}\) rays is of the order of (A) \(10^{-3} \mathrm{~m}\) (B) \(10^{-5} \mathrm{~m}\) (C) \(10^{-10} \mathrm{~m}\) (D) \(10^{-12} \mathrm{~m}\)

Short answer

The wavelength of x-rays falls within the range of approximately \(10^{-10}\) meters to \(10^{-8}\) meters. Comparing the given options, option (C) \(10^{-10} \mathrm{~m}\) is the correct choice as it falls within the x-ray wavelength range.

Step-by-step solution

Recall the wavelength range of x-rays

X-rays have wavelengths in the range of approximately \(10^{-10}\) meters to \(10^{-8}\) meters.

Compare given options to the range of x-ray wavelengths

Now that we know the range of wavelengths for x-rays, let's compare the given options to this range: (A) \(10^{-3} \mathrm{~m}\) - This option is too large to be the wavelength of x-rays. (B) \(10^{-5} \mathrm{~m}\) - This option is also too large for x-ray wavelengths. (C) \(10^{-10} \mathrm{~m}\) - This option falls within the x-ray wavelength range. (D) \(10^{-12} \mathrm{~m}\) - This option is too small to be the wavelength of x-rays.

Choose the correct option

Since option (C) \(10^{-10} \mathrm{~m}\) falls within the range of x-ray wavelengths, it is the correct choice.

Key concepts

Electromagnetic Spectrum

The electromagnetic spectrum is a vast continuum of electromagnetic waves, ranging across varying wavelengths and frequencies. It encompasses everything from radio waves to gamma rays. Each type of wave occupies a specific position within this spectrum.

One critical region of the electromagnetic spectrum is the x-ray region, which plays a vital role in both medical imaging and industrial applications. X-rays generally possess wavelengths ranging from approximately \(10^{-8}\) meters to \(10^{-10}\) meters. This positions them between ultraviolet radiation and gamma rays in the electromagnetic spectrum.

Understanding the place of x-rays in the electromagnetic spectrum helps identify their unique properties such as high energy and ability to penetrate substances, which is why they are crucial in various scientific fields and everyday technologies.

Wavelength Measurement

Wavelength is a key characteristic of any wave, including x-rays. It is defined as the distance between successive crests or troughs of a wave. This measurement can be expressed in meters, a fundamental unit in physics, but often smaller subunits such as nanometers or angstroms are more manageable for x-ray wavelengths.

To measure wavelengths of x-rays, scientists often use complex instruments like x-ray crystallography. Such technology allows us to study the atomic structure of materials while pinpointing precise wavelength sizes in the x-ray spectrum range. Understanding accurate wavelength measurement is integral to various applications such as determining energy levels and identifying material compositions.

By discerning the wavelength, we also ascertain the frequency of the wave, since they are intrinsically linked through the equation: \[ c = \lambda \times f \]where \(c\) is the speed of light, \(\lambda\) is the wavelength, and \(f\) is the frequency.

Recognizing the wavelength is fundamental in distinguishing between different types of electromagnetic radiation.

Physics Problem Solving

Physics problem-solving often involves applying known scientific principles to identify or rectify unknowns, as seen in determining the wavelength of x-rays. This approach is systematic and logical, generally requiring a clear understanding of concepts before invoking problem-solving strategies.

In exercises involving wavelength determination, like the one covered here, recognizing the relevant characteristics of the electromagnetic spectrum is crucial. By identifying that x-ray wavelengths fall within a given range, we apply elimination techniques to ascertain the correct answer.

Effective physics problem-solving entails:

• Recalling fundamental concepts and definitions.
• Comparing given data to known ranges or values.
• Applying equations to relate various properties like frequency and speed if needed.

These strategies help students develop critical thinking skills while encouraging a methodical approach to tackling complex physics problems.