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Chapter 33: Problem 69

Some neodymium-glass lasers can provide \(100 \mathrm{TW}\) of power in \(2.2 \mathrm{~ns}\) pulses at a wavelength of \(0.26 \mu \mathrm{m}\). How much energy is contained in a single pulse?

Short Answer

Expert verified
The energy in a single pulse is 220,000 J (220 kJ).

Step by step solution

01

Understand the Given Values

In this problem, we are given the power of the laser as \(100 \; \text{TW}\) (terawatts) and the duration of the pulse as \(2.2 \; \text{ns}\) (nanoseconds). We need to find out the energy contained in a single pulse.
02

Convert Units

First, we need to convert the power from terawatts (TW) to watts (W) and the time from nanoseconds (ns) to seconds (s).1 TW = \(10^{12}\; \text{W} \), so \(100 \; \text{TW} = 100 \times 10^{12} \; \text{W} \).1 ns = \(10^{-9}\; \text{s} \), so \(2.2 \; \text{ns} = 2.2 \times 10^{-9} \; \text{s}\).
03

Use the Formula for Energy

The energy \(E\) of a pulse can be calculated using the formula \(E = P \times t\), where \(P\) is the power and \(t\) is the time duration of the pulse.
04

Insert the Values

Insert the given values into the energy formula:\[ E = 100 \times 10^{12} \; \text{W} \times 2.2 \times 10^{-9} \; \text{s} \]
05

Calculate the Energy

Multiply the values to find the energy.\[ E = 100 \times 2.2 \times 10^{12} \times 10^{-9} \; \text{J} \]\[ E = 220 \times 10^{3} \; \text{J} \]\[ E = 220,000 \; \text{J} \]
06

Present the Answer

The energy contained in a single pulse is \(220,000 \; \text{J}\), or equivalently, \(220 \; \text{kJ}\) (kilojoules).

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Key Concepts

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

Neodymium-glass lasers
Neodymium-glass lasers are a special type of laser that utilize neodymium ions embedded in a glass matrix to produce high-powered laser emissions. These lasers excel in applications requiring extremely high energy output due to their ability to release energy in short, powerful bursts.
Neodymium-glass lasers are commonly used in industrial and scientific fields. Some of their primary uses include:
  • Cutting and welding in manufacturing processes.
  • Targeting and focusing in scientific research, including nuclear fusion experiments.
  • Medical applications such as laser surgery and skin treatments.
These lasers have a unique property of operating efficiently at various wavelengths, which can be tuned according to the specific needs of the application. Their ability to generate huge amounts of power in very short bursts makes them invaluable in precision tasks.
Power conversion
Power conversion is a crucial step in understanding and using lasers effectively. It involves converting the measurable power of a laser from a seemingly abstract unit to watts, the standard unit of power.
For neodymium-glass lasers, power is often given in terawatts (TW). Here's how the conversion works:
  • 1 terawatt (TW) is equal to \(10^{12}\) watts (W).
  • To convert 100 TW to watts, we multiply: \(100 \times 10^{12} \; \text{W}\).
  • Resulting in a massive \(100,000,000,000,000 \; \text{W}\).
Understanding this conversion is essential for calculating the energy output of a laser pulse and applying this knowledge to practical uses. It allows scientists and engineers to determine how laser energy can be harnessed in real-world applications.
Pulse duration
Pulse duration refers to the time over which a laser emits its energy in a single burst. For neodymium-glass lasers, this duration is often extremely short, measured in nanoseconds (ns).
Consider the following:
  • 1 nanosecond (ns) is \(10^{-9}\) seconds.
  • In our example, the laser pulse lasts \(2.2 \; \text{ns}\).
  • This converts to \(2.2 \times 10^{-9} \; \text{s}\).
Such incredibly brief durations allow the laser to deliver its energy in a compact interval, minimizing waste and maximizing precision. Pulse duration is critical in applications where timing and accuracy are essential, such as in machining or medical procedures.
Wavelength
The wavelength of a laser is the distance between two consecutive peaks of the light wave emitted by the laser. Neodymium-glass lasers operate at specific wavelengths, which determines the color and type of light they produce.
Key points about laser wavelength include:
  • Wavelength is usually measured in micrometers (\(\mu\text{m}\)).
  • The neodymium-glass laser in this exercise has a wavelength of \(0.26 \; \mu\text{m}\).
  • This corresponds to ultraviolet light, which is beyond the visible spectrum for human eyes.
Wavelength is a significant factor in the laser鈥檚 application. Different wavelengths interact uniquely with various materials, making it important to choose the right laser for specific tasks, whether it be cutting, engraving, or medical treatments.

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Most popular questions from this chapter

A catfish is \(1.50 \mathrm{~m}\) below the surface of a smooth lake. (a) What is the diameter of the circle on the surface through which the fish can see the world outside the water? (b) If the fish descends, does the diameter of the circle increase, decrease, or remain the same?

Light that is traveling in water (with an index of refraction of 1.33) is incident on a plate of glass (with index of refraction 1.71). At what angle of incidence does the reflected light end up fully polarized?

A certain helium-neon laser emits red light in a narrow band of wavelengths centered at \(632.8 \mathrm{~nm}\) and with a "wavelength width" (such as on the scale of Fig. 33-1) of \(5.00 \mathrm{pm}\). What is the corresponding "frequency width" for the emission?

Sunlight just outside Earth's atmosphere has an intensity of \(1.40 \mathrm{~kW} / \mathrm{m}^{2}\). Calculate (a) \(E_{m}\), (b) \(B_{m}\), (c) \(E_{\mathrm{rms}}\), and (d) \(B_{\mathrm{rms}}\) for sunlight there, assuming it to be a plane wave.

An airplane flying at a distance of \(10 \mathrm{~km}\) from a radio transmitter receives a signal of intensity \(28 \mu \mathrm{W} / \mathrm{m}^{2}\). What is the amplitude of the (a) electric and (b) magnetic component of the signal at the airplane? (c) If the transmitter radiates uniformly over a hemisphere, what is the transmission power?
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