Question

What is the wavelength range of visible light? (A) \(10 \mathrm{~A}\) to \(100 \mathrm{~A}\) (B) \(4000 \mathrm{~A}\) to \(7000 \mathrm{~A}\) (C) \(8000 \AA\) to \(10000 \AA\) (D) \(10000 \AA\) to \(15000 \AA\)

Short answer

The wavelength range of visible light is given by Option B: \(4000 \mathrm{~A}\) to \(7000 \mathrm{~A}\) (400 nm to 700 nm).

Step-by-step solution

Recall the wavelength range of visible light

The wavelength range of visible light is approximately 400 nm (4,000 Å) to 700 nm (7,000 Å). Now, let's analyze each option:

Option A

\(10 \mathrm{~A}\) to \(100 \mathrm{~A}\) converts to 1 nm to 10 nm. This range does not match the range of visible light.

Option B

\(4000 \mathrm{~A}\) to \(7000 \mathrm{~A}\) converts to 400 nm to 700 nm. This range matches the range of visible light.

Option C

\(8,000 \AA\) to \(10,000 \AA\) converts to 800 nm to 1000 nm. This range is beyond the range of visible light.

Option D

\(10,000 \AA\) to \(15,000 \AA\) converts to 1000 nm to 1500 nm. This range is also beyond the range of visible light. Based on the comparisons above, we can see that only one of the options matches the well-established range of visible light wavelengths.

Conclusion

The wavelength range of visible light is given by Option B: \(4000 \mathrm{~A}\) to \(7000 \mathrm{~A}\) (400 nm to 700 nm).

Key concepts

Electromagnetic Spectrum

The electromagnetic spectrum is a range of all types of electromagnetic radiation. Light, which is only a small part of this spectrum, comes in various forms that include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Each type differs primarily in wavelength and frequency.

- At one end of the spectrum, radio waves have long wavelengths and low frequency. - At the other, gamma rays have short wavelengths and high frequency. Visible light occupies a narrow band in the middle of the spectrum, with wavelengths ranging approximately from 400 to 700 nanometers (nm). This particular band can be detected by the human eye, allowing us to see colors. Light at 400 nm appears violet, while at 700 nm, it appears red.

Understanding the electromagnetic spectrum helps in comprehending how light interacts with materials and how various technologies, such as fiber optics and cameras, work. Despite being a tiny part of the spectrum, visible light plays a crucial role in daily life and numerous scientific applications.

Wavelength Conversion

Converting between units of wavelength is essential in scientific disciplines where precise measurements are necessary, such as physics and chemistry. Since different fields and contexts might use different units, it is crucial to understand how to switch between them easily.

For example, in the context of visible light, wavelengths can be measured in nanometers (nm) or angstroms (Å). The conversion between these units is straightforward:

• 1 nanometer (nm) equals 10 angstroms (Å).

Therefore, a wavelength of 400 nm can also be expressed as 4,000 Å. Similarly, 700 nm converts to 7,000 Å.

Grasping wavelength conversion is vital when dealing with data from various sources that might use different units. It ensures you can accurately interpret and compare findings across diverse scientific literature and experimental work. When analyzing problems, it's always beneficial to double-check unit consistency to avoid misinterpretations.

Nanometers and Angstroms

When studying light and its properties, you'll frequently encounter the units nanometers and angstroms. Both units are used to describe very small lengths, often in the context of wavelengths.

- **Nanometers**: A nanometer is one-billionth of a meter (1 nm = 10⁻⁹ m). Nanometers are commonly used to measure wavelengths in modern scientific research because the scale aligns well with atomic and molecular sizes. - **Angstroms**: An angstrom is one-tenth of a nanometer (1 Å = 10⁻¹⁰ m). Historically, angstroms have been used because they offered a convenient unit for describing the visible spectrum and other small length scales before nanometers became standard in contemporary usage. Using both metrics provides flexibility in describing the same phenomena, as seen in problems involving visible light wavelengths. Whether data is presented in nm or Å, it is helpful to quickly convert and compare them, ensuring measurements are interpreted accurately in any context. Embracing both units helps avoid confusion and enhances comprehension when dealing with the minute scales typical in the study of light and electromagnetic waves.