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

In August 2011, the Juno spacecraft was launched from Earth with the mission of orbiting Jupiter, arriving nearly five years later in July of 2016. The distance between the two planets varies depending on where each planet is in its orbit, but at the closest, the distance between Jupiter and Earth is 391 million miles. What is the minimum amount of time it takes for a transmitted signal from Juno to reach the Earth?

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Identify the speed of light, which is approximately 186,282 miles per second.
Determine the distance the signal needs to travel, which is the closest distance between Jupiter and Earth: 391 million miles.
Use the formula for time, which is time = distance / speed.
Substitute the known values into the formula: time = 391,000,000 miles / 186,282 miles per second.
Calculate the time it takes for the signal to travel from Juno to Earth using the values provided.

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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 (or about 186,282 miles per second). This constant is crucial for calculating the time it takes for signals, such as those transmitted from spacecraft, to travel across vast distances in space.
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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 allows us to determine how long it takes for a signal to travel from one celestial body to another based on the distance and the speed of light.
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Astronomical Units and Distances

Astronomical units (AU) are a standard measure of distance in astronomy, where 1 AU is the average distance from the Earth to the Sun, approximately 93 million miles. Understanding distances in space, such as the 391 million miles between Earth and Jupiter, is essential for calculating travel times for signals and spacecraft.
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Related Practice
Textbook Question

Consider the two waves shown here, which we will consider to represent two electromagnetic radiations: (b) What is the frequency of wave A?

Textbook Question

If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange-yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission. b. What is the energy of 1.00 mol of these photons? (A mole of photons is called an Einstein.)

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 CD player has an output wavelength of 780 nm and a power level of 0.10 mW. How many photons strike the CD surface during the playing of a CD 69 minutes in length?

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?