Planck’s constant
in the light of an
incandescent lamp
Introduction
The idea of light quanta
• Planck (1900): emission of radiant energy by
matter does not take place continuously, but in
finite “quanta of energy” h
(h= Planck’s constant 6.63x10-34 J.s,
 =frequency)
• Einstein (1905): light quanta (photons) as
inherent in the nature of radiation itself
Distribution of intensity of heat radiation
as a function of the wavelength
:
u  
c1

  e

5
c2
T

 1

Emissivity
(=1 for
perfect
black-body
radiation)
C1 , C2 :
Constant
parameters
Planck’s radiation law
Radiation energy per time unit for the wavelength 
u  
c1

5
  e

c2
T
Where

 1

c2=hc/k
h: Planck’s constant
c: velocity of light
k: Boltzmann’s constant
Main objective of
this experiment
Report on the
experiment
Emission of a 12 V tungsten lamp
u
u  
wavelength, 
c1
 c2


5  T
  e  1




The light spectrum emitted by the filament is continuous.
u
u  
wavelength, 
c1
 c2



5  e T  1




A narrow band of the visible spectrum is selected with a
combination of Orange II and Copper Sulphate solution
(it absorbs infrared strongly).
u
u  
wavelength, 
0
Liquid filter
c1
 c2


5  T
  e  1




We will assume that the selected band is nearly monochromatic.
u
u  
wavelength, 
0
Liquid filter
c1
 c2


5  T
  e  1




The wavelength of the selected band is in the spectral response
range of a Light Dependent Resistor (LDR)
u
u  
wavelength, 
0
Liquid filter
c1
 c2


5  T
  e  1




From the formula:
u  
c1
 c2


5  T
  e  1




Block diagram
h
(1)
c2
For small 
lnRldr
u0  
c1
c2
5 0T
(2)
0 e
1/ T
lllumination E on the LDR is
proportional to the transmitted energy
E  u 0
ln R  ln c3 
(3)
Resistance R of LDR
is related to illumination as:
R  b  E 
b: constant
 : parameter
(4)
Plotting
c 2 1
0 T
(6)
Taking logarithms
Combining (2), (3) and (4):
R  c3e
c2 
0T
(5)
Experimental
setup
GENERAL DIAGRAM
Solution
filter
Potentiometer
LDR
Lamp
Ohmeter
Battery
Voltmeter

V
A
Ammeter
COMPONENTS
Battery
Cover
Potentiometer
LDR
Lamp
Platform
Solution filter
Holder

V
A
Grey filter
Ruler
Ohmeter
Voltmeter
Ammeter
INSTALLING
THE
EQUIPMENT
1
Turn the
potentiometer knob
anticlockwise up to
the limit
2
Turn slowly the
tube holder
aligning the
lateral holes
between the
lamp and the
LDR.
3
Move the LDR
towards its lateral
hole, positioning its
surface as the figure
shows.
4
Insert the
solution filter
tube in its holder.
5
Put the cover onto the
platform to protect
from the outside light.
In order to ensure the
correct initial
conditions, LDR
should keep in total
darkness for at least 10
minutes before the
measurements.
Procedure
Some previous
measurements are
needed before using
Equation (6)
c 2 1
ln R  ln c3 
 T
R
(6)
T

0
T Temperature of the emmitting filament
Relation between the
resistance of the filament (RB)
and its temperature (T)
RRB
Experimental data fit
T  aRB
RRB00
0 ,83
I
a can be derived from the filament
resistance (RB0) at room temperature (T0)
T0
a  0.83
RB0
Using the multimeter
as a thermometer.
RB0 can be
extrapolated to I = 0
from measurements
of V and I,
V
A
 transmission of the filter
Solution of:
- Orange II.
- CuSO4 (it absorbs the infrared light).
0 = 590 nm
% transmitance
35
30
25
20
15
10
5
0
450
500
550
600
650
700
750
l/nm
/nm
 Parameter of the LDR
En
Rn  bE 
Rn
Rn
ln '   ln 0.512
Rn
Grey filter
0.512En R ’
n
R  b(0.512 E )
'
n

COLLECTING DATA
R
V
A
I
V
RB=V/I
T = aRB0.83
RB-0.83
R
lnR
I1
V1
RB1
T1
RB1-0.83
R1
lnR1
I2
V2
RB2
T2
RB2-0.83
R2
lnR2
I3
V3
RB3
T3
RB3-0.83
R3
lnR3
In
Vn
RBn
Tn
RBn-0.83
Rn
lnRn
lnR
m
c 2
0 a
RB-0.83
From the slope
lnR
c 2
m
0 a
RB-0.83
We obtain
c2 
m0 a

And finally the Planck´s constant:
kc2
h
c
h: Planck´s constant.
k: Boltzmann´s constant.
c: speed of light.
End of
presentation