EBK LOOSE-LEAF VERSION OF UNIVERSE
EBK LOOSE-LEAF VERSION OF UNIVERSE
11th Edition
ISBN: 9781319227975
Author: KAUFMANN
Publisher: VST
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Chapter 16, Problem 56Q
To determine

The wavelengths of radiation at which the photosphere, chromosphere, and corona emits the most radiation and, using these wavelengths, mention the best way for observing such regions in the solar atmosphere, given that each part of the atmosphere behaves as a perfect blackbody and average temperature for the chromosphere is 50000 K and that for corona is 1.5×106K.

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Answer to Problem 56Q

Solution:

The wavelengths at which the photosphere, chromosphere, and corona emits the most radiation are 500nm, 58nm, and 2nm, respectively.

This result shows that the wavelength of light from photosphere is much larger. So, the observation of photosphere can be possible from Earth, whereas the observation of chromosphere and corona is possible from space station.

Explanation of Solution

Given data:

The temperature of chromosphere is 50000K.

The temperature of corona is 1.5×106K.

Formula used:

Wien’s law is written as,

λmax=bT

Here, λmax is the maximum wavelength, T is the absolute temperature in kelvin, and b is the constant of proportionality which is equal to 2.89×103mK.

Explanation:

Consider the average surface temperature of photosphere to be 5800 K.

Use Wien’s law for writing the expression for wavelength emitted by the photosphere.

λmax,1=bT1

Here, subscript 1 represents the corresponding quantities for photosphere.

Substitute 2.89×103mK for b and 5800K for T1.

λmax,1=2.89×103mK5800K=4.98×107 m(109 nm1 m)500 nm

Since the wavelength of 500nm lies in the range of visible radiation, the photosphere emits visible light radiation.

Use Wien’s law for writing the expression for wavelength emitted by the chromosphere.

λmax,2=bT2

Here, subscript 2 represents the corresponding quantities for chromosphere.

Substitute 2.89×103mK for b and 50000K for T2.

λmax,2=2.89×103mK50000K=5.78×108 m(109 nm1 m)58 nm

Since the wavelength of 58nm lies in the range of ultraviolet radiation, the chromosphere emits ultraviolet radiation.

Use Wien’s law for writing the expression for wavelength emitted by the corona.

λmax,3=bT3

Here, subscript 2 represents the corresponding quantities for corona.

Substitute 2.89×103mK for b and 1.5×106K for T3.

λmax,3=2.89×103mK1.5×106K=1.93×109 m(109 nm1 m)2 nm

Since the wavelength of 2nm lies in the range of x-ray radiation, the corona emits x-ray radiation.

Chromosphere and corona emit light of short wavelength, which is not clearly seen by the observer. For getting a clear picture of corona and chromosphere, space station is used.

Conclusion:

Hence, the wavelengths at which the photosphere, chromosphere, and corona emit the most radiation are 500nm, 58nm, and 2nm, respectively.

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