Solution
Problem 3
What would be the frequency of an electromagnetic wave having a wavelength equal to Earth's diameter? In what part of the electromagnetic spectrum would such a wave lie?
For the Earth’s diameter,
l
= 12,756 km.
c = 300,000 km/s = 12,756 km
´
f.
f = 23.5 Hz.
This wave would be in the extreme long-wavelength radio.
Problem 7
Normal human body temperature is about 37 degrees C. What is this temperature in kelvins?
What is the peak wavelength emitted by a person with this temperature?
In what part of the spectrum does this lie?
37 + 273 = 310°K.
Using Wien’s law,
lmax =
0.29/T, with T in Kelvins and the wavelength in centimeters.
For 310 K, this gives
lmax =
0.00094 cm = 9.4 µm.
This is in
the infrared.
Problem 12
Radiation from the nearby star Alpha Centauri is observed to be reduced in wavelength (after correction for the Earth's orbital motion) by a factor of 0.999933.
What is the recession velocity of Alpha Centauri relative to the Sun?
Use the Doppler formula.
v = 300,000 km/s
´ (1-0.999933),
v =
20 km/s.