/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 71 Find the frequency of blue light... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 71

Find the frequency of blue light with a wavelength of \(460 \mathrm{~nm}\).

Short Answer

Expert verified
The frequency of blue light with a wavelength of \(460 \mathrm{~nm}\) is approximately \(6.52 \times 10^{14} \mathrm{~Hz}\).

Step by step solution

01

Identify the Problem

To find the frequency of blue light, we need to use the relationship between wavelength, frequency, and the speed of light. The speed of light, denoted by \(c\), is a constant \(3.00 \times 10^8\) meters per second.
02

Convert Units

The wavelength given is \(460\) nanometers (\(\mathrm{nm}\)). We need to convert it to meters to use the formula correctly. Remember that \(1 \mathrm{~nm} = 10^{-9} \mathrm{~m}\). So, \(460 \mathrm{~nm} = 460 \times 10^{-9} \mathrm{~m} = 4.60 \times 10^{-7} \mathrm{~m}\).
03

Apply the Formula

The relationship between the speed of light \(c\), frequency \(f\), and wavelength \(\lambda\) is given by the formula: \(c = f \times \lambda\). We can rearrange this to solve for the frequency: \(f = \frac{c}{\lambda}\).
04

Substitute Values and Calculate

Substitute the known values into the formula: \(f = \frac{3.00 \times 10^8 \mathrm{~m/s}}{4.60 \times 10^{-7} \mathrm{~m}}\). Perform the division to find the frequency: \(f \approx 6.52 \times 10^{14} \mathrm{~Hz}\).

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Key Concepts

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

Wavelength
The concept of wavelength is fundamental when discussing waves, such as light. Wavelength, represented by the symbol \( \lambda \), is the distance between consecutive peaks of a wave. It is typically measured in meters, but in the case of light, it is often more convenient to use nanometers. A shorter wavelength corresponds to higher energy in waves like light, which is why blue light, with its short wavelength, is more energetic than red light. Understanding wavelength is key when solving for other properties of waves, like frequency.
Speed of Light
The speed of light is an important constant in physics. Denoted as \( c \), it is the speed at which light travels in a vacuum. This value is approximately \( 3.00 \times 10^8 \) meters per second \( \mathrm{m/s} \). This constant speed links the optical properties of light, such as wavelength and frequency. The formula \( c = f \times \lambda \) is used to describe the relationship between these properties, where \( f \) is frequency. This knowledge helps us calculate one property if we know the others.
Nanometers
Nanometers are a handy unit for measuring very small lengths, such as wavelengths of light. - One nanometer \( (\mathrm{nm}) \) is one-billionth of a meter, \( 10^{-9} \mathrm{~m} \). - Using nanometers makes it easier to express and calculate wavelengths of light, which are often very small numbers when converted to meters. When doing calculations in physics, converting wavelength from nanometers to meters allows for the use of the standard unit of meters in equations, ensuring accuracy and consistency.
Conversion of Units
Unit conversion is crucial in scientifically accurate calculations. In our problem, we converted the wavelength from nanometers to meters to use it in the speed of light formula. - The conversion process involves multiplying the number of nanometers by \( 10^{-9} \), because \( 1\, \mathrm{nm} = 10^{-9} \mathrm{~m} \). It's a straightforward step but absolutely necessary for maintaining the proper units throughout your calculations. Getting comfortable with unit conversions will aid you in correctly using many physics formulas.

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Most popular questions from this chapter

A radar unit in a highway patrol car uses a frequency of \(9.00 \times 10^{9} \mathrm{~Hz}\). What frequency difference will the unit detect from a car approaching the parked patrol car with a speed of \(35.0 \mathrm{~m} / \mathrm{s}\) ? (Hint: The car reflects Doppler shifted waves back to the patrol car. Thus, the radar unit observes the effect of two successive Doppler shifts.)

Triple Choice Suppose the wavelength of a given light source is doubled. Does the frequency of the light increase by a factor of 2 , decrease by a factor of 2 , or remain the same? Explain.

Calculate At this very moment you are giving off electromagnetic waves with a wavelength of about \(9.0\) microns \(\left(9.0 \times 10^{-6} \mathrm{~m}\right)\). (a) What is the frequency of these waves? (b) To what portion of the electromagnetic spectrum do these waves belong?

Triple Choice When a source of light moves toward you, is the frequency of the light you observe greater than, less than, or equal to the frequency of light that the source emits? Explain.

Triple Choice Is the wavelength of infrared waves greater than, less than, or equal to the wavelength of ultraviolet waves? Explain.
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