For question 1: (google "Earths energy budget" to see the figure)
For question 7: (https://www.google.com/search?q=image+of+geometric+framework+for+computing+the+solid+angle+subtended+by+a+sphere&source=lnms&tbm=isch&sa=X&ei=m55EU6zYDablyQGA_YDwAg&ved=0CAYQ_AUoAQ&biw=1440&bih=779#q=solid+angle+subtended+by+a+sphere+of+radius+R&tbm=isch&facrc=_&imgdii=_&imgrc=ksLhL2vcOnsjSM%253A%3BHTZYbTWQZV0UlM%3Bhttp%253A%252F%252Fi.stack.imgur.com%252FztHhd.png%3Bhttp%253A%252F%252Fstackoverflow.com%252Fquestions%252F3717226%252Fradius-of-projected-sphere%3B381%3B512)
1. avg over the globe, about 342 Wm^-2 of solar radiation is incident on the top of the earth's atmosphere. Using the info in the figure compute the avg rate at which the atmosphere (including clouds) would be heated by direct absorption of solar radiation if there were no other processes at work. Combine these with the rate of absorbed solar radiation to find a value that can be expressed in degrees per day.
You can use these values to help: (g) 9.81 ms^-2, (cp) 1004 J kg^-1K^-1, (po) 1.013 x 10^5 Pa
2. visible light has a wavelength of approx 0.5 um. What is its frequency in Hz? EM radiation has a frequency of approx 3GHz, what is its wavelength in centimeters? AC electrical current has a frequency of 60Hz, what is its wavelength in km?
4. For red light (lamda = 0.64um), ni in pure water is approx 1.3 x 10^-8; for blue light (lamda = 0.48um), ni is approx 1.0x10^-9. The deep end of a typical home swimming pool is approx 2.5m deep. Compute the fraction of each wavelength that survives the two-way trip to the bottom of the pool and back, when illuminated (and viewed) from directly above. In light of your findings and in view of the appearance of most swimming pools as seen from the air, comment on the common assumption that water is "colorless"
5. Only radiation with wavelengths smaller than 0.2424um is capable of dissociating molecular oxygen into atomic oxygen, according to the reaction: O2 + photon ----> O + O. Based on this info, how much energy is apparently required to break the molecular bond of a single molecule of O2
6. Consider a cloud that, when viewed from a point on the surface, occupies the portion of the sky defined by: pi/4 < theta < pi/2 and 0 < flux < pi/8. What is the solid angle subtended by the cloud? What percentage of the sky is covered by this cloud?
7. The moon is at a mean distance Dm = 3.84 x 10^5km from the earth; the sun is at a mean distance Ds = 1.496 x 10^8km. The radius of the moon is Rm = 1.74x10^3km; the radius of the sun is Rs = 6.96 x10^5km. Compute the angular diameter in degrees subtended by the sun and the moon. You can Refer to a figure online for help. Compute the solid angle subtended by the sun and the moon. Which appears larger from the Earth, and by what percentage do the two soling angles differ? If the above values were constant, would it be possible to explain the occurrence of total solar eclipses?