Spring 2005
Dr. Mike Fanelli
Solutions for Assigned Problems
Chapter 16
PROBLEM 16-2:
Given the temperatures at (a) the core of the Sun, (b) in the convective zone,
and, (c) at the base of the photosphere, determine the wavelength of the peak of
the blackbody curve at each location.
ANSWER: Wien’s law defines the blackbody peak as a function of temperature.
In chapter 3, the “more precisely” box 3-2 describes Wien’s law and gives the
relationship.
(max)
= 0.29  temperature,
Where (max) is the peak wavelength of emission for a blackbody at the given
temperature, with wavelength expressed in centimeters.
(a) Core of the Sun:
(max)
= 0.29  107 K = 2.9 x 10-8 cm = 2.9 Angstroms.
This wavelength is in the X-ray portion of the electromagnetic spectrum
(b) Convective zone:
(max)
= 0.29  105 K = 2.9 x 10-6 cm = 290 Angstroms
This wavelength is in the extreme UV portion of the EM spectrum.
(c) Base of the photosphere: (max) = 0.29  104 K = 2.9 x 10-5 cm = 2900
Angstroms
This wavelength is in the far ultraviolet, just blueward of the shortest wavelength
violet light which passes through Earth’s atmosphere.
PROBLEM 16-12:
Given the rate of mass lost in the solar wind, how long will take for all of the
Sun’s mass to be lost ?
ANSWER: This problem deals with a rate – the rate of mass loss by the Sun
each second in the solar wind. It is equivalent to determining the time it would
take to travel a fixed distance, given a rate of travel. For example, how long
would it take you to travel 1000 miles at 30 miles per hour ? In this problem, the
question is, how long will take for all of the Sun’s mass to “leave” in the solar
wind, given a specific rate, 2 million tons per second ? The Sun’s mass is given
in the “Sun Data” box in section 16.1.
Mass of the Sun  rate of mass loss =
2 x 1030 kilograms
 2 x 109 kilograms per second
= 1021 seconds = 3.2 x 1013 years = 32 trillion years.
This period is a substantially longer time then the age of the universe.
PROBLEM 16-13:
Given the rate of mass lost in the solar wind, how long will take for the Sun to
emit one Earth mass of material ?
ANSWER: This problem is a variation of the previous one. The Earth’s mass is
given in Appendix 3 in the back of the book.
Mass of the Earth  rate of mass loss =
6 x 1024 kilograms  2 x 109 kilograms per second
= 3  1015 seconds = 9.5 x 107 years = 95 million years.
Still a long time.