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Chapter 37: 39P (page 1148)

A spaceship is moving away from Earth at speed 0.20c. A source on the rear of the ship emits light at wavelength 450 nm according to someone on the ship. What (a) wavelength and (b) color (blue, green, yellow, or red) are detected by someone on Earth watching the ship?

Short Answer

Expert verified

(a) The radial speed NGC7319 relative to Earth is 0.023c.

(b) The color of light detected on Earth is Yellow.

Step by step solution

01

Identification of given data

The speed of spaceship is $v = 0.20 c$

The wavelength of light emitted from rear end of ship is $位_{o} = 450 nm$

The speed for the variation in the colour of light from red to green is found by using the formula for Doppler shift.

02

Determination of wavelength of light detected on Earth

(a)

The wavelength of light detected on Earth is given as:

$位 = 位_{o} \sqrt{\frac{1 + (\frac{v}{c})}{1 - (\frac{v}{c})}}$

Here, c is the speed of light.

Substitute all the values in the above equation.

$\begin{array}{rcl} 位 & = & (450 nm) \sqrt{\frac{1 + (\frac{0.20 c}{c})}{1 - (\frac{0.20 c}{c})}} \\ = & 550 nm \end{array}$

Therefore, the wavelength of light detected on Earth is 550 nm.

03

Identification color of light detected on Earth

(b)

The wavelength of the light detected on Earth falls under the yellow color of the visible spectrum so the color of light detected on Earth is Yellow.

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Most popular questions from this chapter

A Foron cruiser moving directly toward a Reptulian scout ship fires a decoy toward the scout ship. Relative to the scout ship, the speed of the decoy is $0.980 c$ and the speed of the Foron cruiser is $0.900 c$ . What is the speed of the decoy relative to the cruiser?

How much work is needed to accelerate a proton from a speed of 0.9850c to a speed of 0.9860c?

Spatial separation between two events. For the passing reference frames of Fig. 37-25, events A and B occur with the following spacetime coordinates: according to the unprimed frame, $(x_{A}, t_{A})$ and role="math" localid="1663045013644" $(x_{B}, t_{B})$ according to the primed frame, $({x^{'}}_{A}, {t^{'}}_{A})$ androle="math" localid="1663045027721" $({x^{'}}_{B}, {t^{'}}_{B})$ . In the umprimed frame $螖迟 = t_{B} 鈭� t_{A} = 1 .00 鈥坝约$ androle="math" localid="1663045143133" $螖虫 = x_{B} 鈭� x_{A} = 240 鈥尘$ .(a) Find an expression forin ${螖虫}^{'}$ terms of the speed parameter $尾$ and the given data. Graph ${螖虫}^{'}$ versus $尾$ for two ranges of $尾$ : (b) $0$ to $0.01$ and (c) $0.1$ to $1$ . (d) At what value of $尾$ is ${螖虫}^{'} = 0$ ?

In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth鈥檚 atmosphere, 120 km above sea level, a pion is created. The pion has a total energy E of $1.35 脳 10^{5} MeV$ and is travelling vertically downward. In the pion鈥檚 rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth鈥檚 reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV.

The mass of an electron is $9.10938188 脳 10^{- 31} kg$ . To six significant figures, find (a) data-custom-editor="chemistry" $纬$ and (b) data-custom-editor="chemistry" $尾$ for an electron with kinetic energy K = 100.000 MeV.

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