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Chapter 1: Problem 41

The distance between two adjacent peaks on a wave is called the wavelength. (a) The wavelength of a beam of ultraviolet light is 247 nanometers (nm). What is its wavelength in meters? (b) The wavelength of a beam of red light is \(6760 \mathrm{pm}\). What is its wavelength in angstroms (A)?

Short Answer

Expert verified
(a) \(2.47 \times 10^{-7}\) meters; (b) 676 A

Step by step solution

01

Convert Wavelength from Nanometers to Meters

Given the wavelength of ultraviolet light is 247 nm. To convert this to meters, use the conversion factor where 1 nm = \(10^{-9}\) meters.
02

Calculation for Part (a)

Multiply 247 by \(10^{-9}\) to convert nanometers to meters.\[ 247 \, \text{nm} = 247 \times 10^{-9} \, \text{meters} \]
03

Result for Part (a)

The wavelength of ultraviolet light in meters is \(2.47 \times 10^{-7}\) meters.
04

Convert Wavelength from Picometers to Angstroms

Given the wavelength of red light is 6760 pm. To convert this to angstroms (A), use the conversion factor where 1 A = \(10 \, \text{pm}\).
05

Calculation for Part (b)

Divide 6760 by 10 to convert picometers to angstroms.\[ 6760 \, \text{pm} = \frac{6760}{10} \, \text{A} \]
06

Result for Part (b)

The wavelength of red light in angstroms is 676 A.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

wavelength
Understanding wavelength is key to solving many problems in physics, especially those related to waves and light. The wavelength is simply the distance between two consecutive peaks (or troughs) of a wave. It's a measure of the length of one complete cycle of the wave. Whether it's sound waves, light waves, or other electromagnetic waves, the concept of wavelength plays a crucial role in determining their behavior. In general, shorter wavelengths mean higher frequencies and potentially more energy, while longer wavelengths correspond to lower frequencies and less energy.
nanometers to meters
Converting from nanometers to meters is a common task, especially when dealing with the properties of light. The prefix 'nano-' signifies that the measurement is one billionth of a meter, or 10-9 meters. This conversion is straightforward once you understand the relationship:
  • 1 nanometer (nm) = 10-9 meters (m)
For example, if we need to convert the wavelength of a beam of ultraviolet light given as 247 nm into meters, we would perform the following calculation:

247 nm * 10-9 m/nm = 2.47 * 10-7 m.

The result tells us that the wavelength of this ultraviolet light is 2.47 * 10-7 meters.
picometers to angstroms
Switching between picometers and angstroms can also be necessary in various scientific fields. Here’s a simple rule to remember:
  • 1 angstrom (A) = 10 picometers (pm)
This means that you can convert from picometers to angstroms by dividing the value in picometers by 10. For instance, if a wavelength of red light is given as 6760 pm, we convert it to angstroms as follows:

6760 pm ÷ 10 pm/A = 676 A.

This conversion tells us that the wavelength of the red light is 676 angstroms, giving us a convenient way to express the measurement.

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Most popular questions from this chapter

Which of the following include exact numbers? (a) The speed of light in a vacuum is a physical constant; to six significant figures, it is \(2.99792 \times 10^{8} \mathrm{~m} / \mathrm{s}\) (b) The density of mercury at \(25^{\circ} \mathrm{C}\) is \(13.53 \mathrm{~g} / \mathrm{mL}\) (c) There are \(3600 \mathrm{~s}\) in \(1 \mathrm{~h}\). (d) In 2018 , the United States had 50 states.

Bromine is used to prepare the pesticide methyl bromide and flame retardants for plastic electronic housings. It is recovered from seawater, underground brines, and the Dead Sea. The average concentrations of bromine in seawater \((d=1.024 \mathrm{~g} / \mathrm{mL})\) and the Dead Sea \((d=1.22 \mathrm{~g} / \mathrm{mL})\) are \(0.065 \mathrm{~g} / \mathrm{L}\) and \(0.50 \mathrm{~g} / \mathrm{L},\) respectively. What is the mass ratio of bromine in the Dead Sea to that in seawater?

Carry out each calculation, paying special attention to significant figures, rounding, and units \((J=\) joule, the \(S I\) unit of encrgy; mol = mole, the SI unit for amount of substance): (a) \(\frac{\left(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(2.9979 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{489 \times 10^{-9} \mathrm{~m}}\) (b) \(\frac{\left(6.022 \times 10^{23} \text { molecules } / \mathrm{mol}\right)\left(1.23 \times 10^{2} \mathrm{~g}\right)}{46.07 \mathrm{~g} / \mathrm{mol}}\) (c) \(\left(6.022 \times 10^{23}\right.\) atoms \(\left./ \mathrm{mol}\right)\left(1.28 \times 10^{-18} \mathrm{~J} /\right.\) atom \()\left(\frac{1}{2^{2}}-\frac{1}{3^{2}}\right)\) where the numbers 2 and 3 in the last term are exact

The average radius of a molecule of lysozyme, an enzyme in tears, is \(1430 \mathrm{pm}\). What is its radius in nanometers (nm)?

Liquid nitrogen is obtained from liquefied air and is used industrially to prepare frozen foods. It boils at \(77.36 \mathrm{~K}\). (a) What is this temperature in \({ }^{\circ} \mathrm{C} ?\) (b) What is this temperature in \({ }^{\circ} \mathrm{F}\) ? (c) At the boiling point, the density of the liquid is \(809 \mathrm{~g} / \mathrm{L}\) and that of the gas is \(4.566 \mathrm{~g} / \mathrm{L}\). How many liters of liquid nitrogen are produced when \(895.0 \mathrm{~L}\) of nitrogen gas is liquefied at \(77.36 \mathrm{~K} ?\)
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