Q42P The Sun is approximately an idea... [FREE SOLUTION]

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Chapter 38: Q42P (page 1183)

The Sun is approximately an ideal blackbody radiator with surface temperature of 5800 K.
(a) Find the wavelength at which its spectral radiancy is maximum and
(b) identify the type of magnetic wave corresponding to that wavelength.
(c) As we shall discuss in chapter 44, the universe is approximately an ideal blackbody radiator with radiation emitted when atoms first formed. Today the spectral radiancy of that radiation peaks at a wavelength of 1.06 mm (in the microwave region). What is the corresponding temperature of the universe?

Short Answer

Expert verified

Thus, (a) the wavelength of spectral radiancy is maximum at $0.0388 鈥塶尘$ .

(b) the wavelength is $1.24 鈥夆赌媙尘$ .

Step by step solution

(a) The wavelength of spectral radiancy is maximum.

Use the value $h c = 1240 鈥媏痴鈰� nm$ formula then it gives;

$\begin{matrix} 位 = \frac{h}{p} \\ = \frac{h}{\sqrt{2 m_{e} K}} \\ = \frac{h c}{\sqrt{2 m_{e} c^{2} K}} \\ = \frac{1240}{\sqrt{2 (511000) (1000)}} \\ = 0.0388 鈥塶尘 \end{matrix}$

Hence, the wavelength of spectral radiancy is maximum at $0.0388 鈥塶尘$ .

(b) The type of magnetic wave corresponding to the wavelength.

A photon鈥檚 de Broglie wavelength is equal to its familiar wave relationship value. Use the value $h c = 1240 鈥媏痴鈰� nm$ gives:

$\begin{matrix} 位 = \frac{h c}{E} \\ = \frac{1240 e V 鈰� 鈥� n m}{1.00 鈥� k e V} \\ = 1.24 鈥夆赌媙尘 \end{matrix}$

Hence, the wavelength is $1.24 鈥夆赌媙尘$ .

(c) The corresponding temperature of universe.

The neutron mass equals to $1.675 脳 10^{鈭� 27} k g$ . Using the conversion from electronvolts to Joules gives;

$\begin{matrix} 位 = \frac{h}{\sqrt{2 m_{n} K}} \\ = 鈭� \frac{(6.63 脳 10^{鈭� 34} J 鈰� s)}{\sqrt{2 (1.675 脳 10^{鈭� 27} k g) (1.6 脳 10^{鈭� 16} J)}} \\ = 9.06 脳 10^{鈭� 13} 鈥� m \end{matrix}$

Hence, the wavelength of neutron is $9.06 脳 10^{鈭� 13} 鈥� m$ .

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Short Answer

Step by step solution

(a) The wavelength of spectral radiancy is maximum.

(b) The type of magnetic wave corresponding to the wavelength.

(c) The corresponding temperature of universe.

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