Homework 4 Solutions
1a.
Room temperature corresponds to
k T
=
4.05 × 10
‐
21
Joules
. Photons of this energy would have
frequency
f
=
E/h
=
6.11 × 10
12
Hz
and wavelength
λ
=
c/f
=
49.1 microns
.
Is it reasonable that a hot body starts to glow around 1000°C? Wien’s displacement law tells us that the
peak wavelength of a blackbody depends on its temperature:
nm
2276
K
1273
K
m
10
898
.
2
3
peak
=
×
=
=
−
T
b
λ
The peak wavelength is outside the visible range, but there will be a distribution of photon wavelengths
emitted. From the calculation here,
yes
, it’s reasonable that a hot body would just start to have enough
photons of sufficiently short wavelength that we could see a reddish glow at this temperature.
In fact, if we look this up, we can find the blackbody distribution:
(source:
http://en.wikipedia.org/wiki/Wien's_displacement_law
and
http://en.wikipedia.org/wiki/Black_body_spectrum
)
The chart shows that objects start to glow around 1000, which is pretty close to 1273 K, so yes, it’s
reasonable that a hot body would start to glow around 1000°C.

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1b.
flux ൌ ܬ ൌ 1.6 כ 10
ିଵ
W
୫
మ
ߣ ൌ 560 nm
ܧ ൌ ݄݂݊ ൌ
݄݊ܿ
ߣ
ܧ ൌ ܬݐܣ
୮୳୮୧୪
ൌ ܬݐߨݎ
ଶ
Let’s say the diameter of a pupil is 4 mm (this seems reasonable according to
http://en.wikipedia.org/wiki/Pupil
)
Solve for
n
:
݊ ൌ
ܬ ݐ ܣ ߣ
݄ ܿ
ൌ
ܬ ݐ ߨ ݎ
ଶ
ߣ
݄ ܿ
݊ ൌ
൬1.6 כ 10
ିଵ
joule
s m
ଶ

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