Question

For the period \(1960-1983\), the meter was defined to be \(1,650,763.73\) wavelengths of a certain orange-red light emitted by krypton atoms. Compute the distance in nanometers corresponding to one wavelength. Express your result using the proper number of significant figures.

Short answer

One wavelength of the krypton light corresponds to approximately \(0.605\) nanometers when rounded to the appropriate number of significant figures.

Step-by-step solution

Identify the given measurements

The exercise gives a distance: one meter, defined as \(1,650,763.73\) wavelengths of light, and a conversion factor: one meter is equal to \(1x10^{9}\) nanometers.

Calculate the length of one wavelength in meters

Divide one meter by the number of wavelengths it contains. Using the value given in the problem, this gives \(1/1,650,763.73\) meters per wavelength.

Convert the length of the wavelength from meters to nanometers

To convert to nanometers, multiply by the conversion factor given above. This gives \((1/1,650,763.73) * (1x10^{9})\) nanometers per wavelength.

Round to the proper number of significant figures

The measurement given in the problem has six significant figures, so the final result should also have six significant figures.

Key concepts

Wavelength Measurement

Wavelength measurement is crucial in physics for understanding the nature of different forms of electromagnetic radiation, such as light, radio waves, and X-rays. The wavelength of light is the distance between two consecutive peaks or troughs in a wave, and it is often measured in nanometers (nm) for visible light. To measure the wavelength accurately, physicists use devices like spectrometers, which can disperse light into its component wavelengths and detect their individual lengths.

An important aspect of wavelength measurement is keeping track of significant figures, as they represent the precision of the measurement. In our example exercise, the meter was formerly defined by the wavelength of krypton light, reflecting the precision with which scientists could measure this wavelength. The significant figures tell us how confidently each digit in a measurement can be trusted and are useful for comparing the accuracy of different measurements.

Nanometers Conversion

In physics and nanotechnology, the nanometer (m) serves as a common unit for expressing very small lengths, such as the wavelengths of light or the size of atoms. One nanometer is one-billionth of a meter (m). Understanding how to convert between meters and nanometers is essential for comparing measurements taken in different units or scales.

To convert a length from meters to nanometers, you would typically multiply by the conversion factor of one billion m. It's important to make sure that the conversion is done correctly by keeping track of significant figures. In our illustrative exercise, expressing the result with six significant figures maintains the precision dictated by the original meter definition in terms of krypton wavelength.

Units of Length in Physics

Units of length in physics range from the very small, like nanometers, to the incredibly vast, such as light-years. Understanding the range of units and when to use them is fundamental in physics calculations. Small lengths like atomic sizes are often measured in nanometers, while larger lengths might be measured in meters or kilometers.

When dealing with conversions between units, the consistency of units across a calculation is key. Using the correct number of significant figures ensures that the precision of the measured or calculated values is not overstated or understated. In the historical context, the definition of a meter in terms of krypton wavelengths and its conversion to nanometers are perfect examples of the meticulous nature required when working with units of length.