a) Consider a 100 Watt (
) light bulb with a Tungsten
(melting temperature 3683
) filament. Assuming that the bulb is
designed to operate at 
, and that nearly all of the 100
Watt of electrical power consumed by the bulb is converted to
thermal radiation. What then must be the surface area A of the
filament in 
? (Hint: Stefan's constant is 
-
.) Explain whether your result
for A is reasonable from what you would expect the area of a
filament to be.
b) What fraction of the thermal radiation from the bulb falls in the
visible part of the spectrum (
)?
Do you consider the incandescent bulb to be an energy
efficient light source?
Hints: Change variables to express the integral in the form 
, and then make (and justify by
giving an error estimate) the approximation 
. Also, as mentioned in the lecture notes on Black Body
radiation,
as may be derived by a power series expansion of the denominator. Finally, you may wish to have the values
c) The same bulb is then used as the light source in a photoelectric
effect apparatus with a metal target with work function 
and
surface area 
placed D = 10 cm away from, and directly
facing, the bulb. How many photons per second, 
with frequencies in the interval 
hit the target?
Assuming that all photons in this problem that are capable of ejecting
an electron from the surface do so and that all of these electrons are
eventually collected by the electrode, what will be the maximum
saturation current (in units of 1 
) observed in the experiment? (You may use the same type
of approximation you developed in part (b)).