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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition · 1596 pages

ISBN: 9780321973610

Chapter 6: Q63P (page 1251)

One of the wavelengths of light emitted by hydrogen atoms under normal laboratory conditions is $λ = 656.3 n m$ in the red portion of the electromagnetic spectrum. In the light emitted from a distant galaxy this same spectral line is observed to be Doppler-shifted to $λ = 953.4 n m$ in the infrared portion of the spectrum. How fast are the emitting atoms moving relative to the earth? Are they approaching the earth or receding from it?

Short Answer

Expert verified

$107 \times 10^{6} m / s$ The speed of emitting atoms moving relative to the earth is .

Step by step solution

01

Definition of light year

The term light year may be defined as the light travel in one year.

02

Determine the speed

The speed of the atoms can be calculated by the relation as

$u = \frac{c f_{0}^{2} - c f^{2}}{f_{0}^{2} + f^{2}}$

And the relation between frequency and wavelength is $f = \frac{1}{λ}$

$u = \frac{c {(\frac{1}{λ_{0}})}^{2} - c {(\frac{1}{λ})}^{2}}{{(\frac{1}{λ_{0}})}^{2} - {(\frac{1}{λ})}^{2}}$

Now put the values

$u = \frac{(3 \times 10^{8} m / s) (\frac{1}{656.3 \times 10^{- 9} m}) - (3 \times 10^{8} m / s) (\frac{1}{953.4 \times 10^{- 9} m})}{{(\frac{1}{656.3 \times 10^{- 9} m})}^{2} + {(\frac{1}{953.4 \times 10^{- 9} m})}^{2}} u = 107 \times 10^{6} m / s$

Hence, the speed of emitting atoms moving relative to the earth is $107 \times 10^{6} m / s$ .

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Most popular questions from this chapter

In classical (Newtonian) mechanics, the total energy E of a particle can never be less than the potential energy U because the kinetic energy K cannot be negative. Yet in barrier tunneling a particle passes through regions where E is less than U. Is this a contradiction? Explain.

Under what conditions does the magnitude of the average velocity equal the average speed?

During the photoelectric effect, light knocks electrons outof metals. So why don’t the metals in your home lose their electrons when you turn on the lights?

The bonding of gallium arsenide ( $GaAs$ ) is said to be $31 %$ ionic and $69 %$ covalent. Explain.

When a monochromatic light source moves toward an observer, its wavelength appears to be shorter than the value measured when the source is at rest. Does this contradict the hypothesis that the speed of light is the same for all observers? Explain.

See all solutions

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