Question

Wave length of light radiation \(0.000015 \mathrm{~m}=\ldots \ldots \ldots \ldots .\) (a) 15 micron (b) \(1.5\) micron (c) 150 micron (d) \(0.15\) micron

Short answer

The correct representation of the given wavelength in microns is (a) 15 micron.

Step-by-step solution

Convert meters to microns

To convert meters to microns, we need to know that 1 meter is equal to 1,000,000 (1 million) microns. So, we need to multiply the given wavelength in meters by 1,000,000 to find the wavelength in microns. Given wavelength: \(0.000015 \mathrm{~m}\) Conversion factor: \(1 \mathrm{~m} = 1,000,000 \mathrm{~\mu m}\) Now, we multiply the given wavelength in meters by the conversion factor: Wavelength in microns: \(0.000015 \mathrm{~m} * 1,000,000 \mathrm{~\mu m/m} = 15 \mathrm{~\mu m}\)

Compare the result to the given options

Now, we can compare the calculated wavelength in microns (15 microns) to the given options: (a) 15 micron (b) 1.5 micron (c) 150 micron (d) 0.15 micron The correct option is (a) 15 micron, since it matches our calculated wavelength.

Key concepts

Micron Conversion

Micron conversion is an essential concept in understanding the scale of measurements, especially in scientific fields dealing with light and small distances. When converting wavelengths from meters to microns, it is crucial to know the conversion factor: 1 meter equals 1,000,000 microns. This factor allows us to translate large units (meters) into more manageable and relatable units (microns) for tiny wavelengths. For example, the given wavelength in meters is 0.000015 m. By multiplying this value by 1,000,000, we effectively shift the decimal point six places to the right, converting it to 15 microns. Converting small scale measurements like this is often necessary in optics and other fields dealing with microscopic scales, where precision is key.

Light Radiation

Light radiation refers to the energy emitted in the form of waves or particles, which we can often measure in terms of wavelength. Wavelength is the distance between two consecutive peaks or troughs of a wave and is critical in defining the properties of light such as color and intensity. Visible light, which the human eye can detect, falls within a specific range of wavelengths. However, light radiation encompasses a broader spectrum including ultraviolet light and infrared. Understanding the wavelength of light radiation helps in applications like spectroscopy, where these wavelengths can identify substances and materials. The process of determining the wavelength of light often requires unit conversions, such as converting a given range from meters to a smaller unit like microns. This is because the wavelength of light is typically very small, making meters a less practical unit.

Unit Conversion Steps

Unit conversion steps are systematic procedures used to convert one unit of measurement into another, ensuring accuracy and consistency. These steps are crucial in scientific calculations where precision is essential. To successfully convert units, follow these general steps:

• Identify the units you have and the units you need to convert to.
• Understand and apply the appropriate conversion factor. For example, in the exercise, 1 meter equals 1,000,000 microns.
• Multiply or divide as required by the conversion factor to change the original value to the targeted unit.

In the original exercise, we used these steps to convert 0.000015 meters to microns, realizing the answer as 15 microns. Always double-check your calculations after completing your conversion to ensure accuracy, especially when comparing to given options or practicing with multiple-choice problems. These steps are not only useful for light wavelength problems but in any unit conversion tasks across different scientific domains.