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Ch.6 - Electronic Structure of Atoms
Chapter 6, Problem 84

In January 2006, the New Horizons space probe was launched from Earth with the mission to perform a flyby study of Pluto. The arrival at the dwarf planet was estimated to happen after nine years, in 2015. The distance between Earth and Pluto varies depending on the location of the planets in their orbits, but at their closest, the distance is 4.2 billion kilometers (2.6 billion miles). Calculate the minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth.

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Identify the speed of light in a vacuum, which is approximately 299,792 kilometers per second (km/s).
Determine the minimum distance between Earth and Pluto, given as 4.2 billion kilometers.
Use the formula for time, which is time = distance / speed, to calculate the time it takes for a signal to travel from Pluto to Earth.
Substitute the known values into the formula: time = 4.2 billion kilometers / 299,792 km/s.
Perform the division to find the time in seconds, which will give you the minimum time it takes for a signal to travel from Pluto to Earth.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Speed of Light

The speed of light in a vacuum is approximately 299,792 kilometers per second (km/s). This constant is crucial for calculating the time it takes for signals, such as those from space probes, to travel across vast distances in space. Understanding this speed allows us to determine how long it takes for light, or any electromagnetic signal, to traverse the distance between two points, such as Pluto and Earth.
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Speed of Light Formula

Distance and Time Relationship

The relationship between distance, speed, and time is described by the formula: time = distance/speed. In the context of space communication, this formula helps us calculate how long it takes for a signal to travel from one celestial body to another. By knowing the distance to Pluto and the speed of light, we can easily compute the minimum time required for a signal to reach Earth.
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Astronomical Units and Distances in Space

Distances in space are often measured in astronomical units (AU), where 1 AU is the average distance from the Earth to the Sun, approximately 149.6 million kilometers. Understanding these units is essential for grasping the vast scales involved in space exploration. When calculating signal travel time, converting distances into a consistent unit, such as kilometers, is necessary for accurate computations.
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Related Practice
Textbook Question

If a sample of calcium chloride is introduced into a nonluminous flame, the color of the flame turns to orange (“flame test”). The light is emitted because calcium atoms become excited; their return to the ground state results in light emission. (c) Calculate the energy gap between the excited and ground states for the calcium atom.

Textbook Question

Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm (a) Determine which of these emissions occur in the ultraviolet part of the spectrum.

Textbook Question

Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm (c) When burned, a sample of an unknown substance is found to emit light of frequency 6.58 × 1014 s-1. Which of these elements is probably in the sample?

Textbook Question

The watt is the derived SI unit of power, the measure of energy per unit time: 1 W = 1 J>s. A semiconductor laser in a DVD player has an output wavelength of 650 nm and a power level of 5.0 mW. How many photons strike the DVD surface during the playing of a DVD 90 minutes in length?

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Textbook Question

In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labeled 'n0' corresponds to light with a wavelength of 542 nm. (a) What is the value of n0 in s - 1?