-1-
Experiment no. – 10
Planck’s constant ‘h’ solar cell
Object: Determination of Planck’s constant ‘h’ by measuring radiation in a fixed
spectral range.
Apparatus used: The complete experimental arrangement as shown in figure (1) consists
of filament bulb, its power supply (0-12 V d.c.) , A solar cell fitted on mini optical bench,
one Ammeter ( 0- 2 A) and one voltmeter (0-10 V) to read filament current and voltage,
one digital D.C. Microammeter (0-200 μA.).
Filament Bulb
Solar Cell
Figure 1(a)
Filament
Current
A
Filament
Power
Supply
Filament
Voltage
Current
Control
V
Figure 1(b)
Theory: For a black body at temperature ‘T’ the total radiations as well as the spectral
distribution for this radiation are functions of temperature T alone. The spectral
distribution involves Planck’s constant ‘h’.
1
8hc 
hc

E  d  5 exp(
)  1 d
kT
 

………………….1
Working with visible light and temperature upto 2500 oK , we have,
Hence equation (1) simplifies to,
hc
>>1.
 kT
-2E  d 
8hc

5
exp( 
hc
)d
kT
………………….2
If the radiation is received through a filter on a photocell and galvanometer response θ is
measured, we get:
B
hc
)d
………………….3
  8hcA 5 exp(
kT

Where A is a factor depending on geometry of the arrangement and sensitivity of the
galvanometer and Bλ is a function of λ which includes (i) transmission characteristics of
the filter and (ii) wavelength wise response of the photocell. The integral has to cover all
range of λ for which Bλ is non zero.
5000
6000 7000
λ (Α˚)
Bλ
T
R
If we have filter, which has, transmission characteristics schematically represented by
figure 2 (a) and a photovoltaic cell with response schematically represented in figure 2
(b) then the Bλ function is given by products of ordinates T and R plotted against
respective values figure 2 (c).
5000 6000 7000
λ (Α˚)
(a)
(b)
5000
6000
λ (Α˚)
(c)
Figure 2
However, if the filter has a narrow transmission band, one may reduce equation (3) to ,
  8hcAC exp( 
0
hc
)0
kT
………………….4
Where λ0 is some effective mean wavelength , Δ λ0 is the effective band width and C λ0 is
a constant depending on λ0.
At two different temperatures , we get
-3-
 hc 1 1 
2
 exp 
(  )
1
 0 k T1 T2 
………………….5
Where the constant A, B λ and Δ λ0 all cancel out due to the simplifying assumptions
made to go from (3) to (4)
We note that unless the transmission band is narrow, the theory would not hold, further
effective λ0 is not just the center of transmission band of the filter, but it will be seriously
effected by response curve of the photocell. In the photo voltaic cell the shift usually will
hc
) increases
be towards longer wavelength. Even more seriously the term exp( 
kT
rapidly with increasing λ. For T = 2000 0K, as we pass from λ = 5000 0A to λ = 7000 0A.
This exponential term increases from exp(-3) to exp.(-2). This fact will also place
effective λ0 on the higher side of the mean transmission wavelength of the filter.
With in these limitation equation (5) gives
2.303 log 10  = 
hc 1
0 k T
………………….6
Thus log θ vs 1/T graph should be a straight line from whose slope we may deduce h.
2.3030 k (log 10  )
.
………………….7
1
c
( )
T
The experimental task reduces to measure θ for different temperatures of the filament
keeping the geometry and λ0 constant.
METHOD:(a) To determine the value of Rg and Rt/Rg with the V-I characteristics of Bulb.
h
1. To find Rg the resistance of the filament bulb when it just starts glowing: Connect
the set-up with the mains and switched it ON. Apply filament current by the power
supply control knob marked CONTROL on the panel such that the filament just starts
glowing. Note the corresponding filament current and voltage and record these
readings in table-I as shown below. Take at least three readings to the get the better
value of Rg. Refer fig. 3
TABLE: - I For Rg, the resistance of the filament when it just starts glowing.
S.No.
1.
2.
3.
Filament Current
I Amp.
Filament Voltage
V Volt
Rg Ohm
Average Rg
-4-
2. To find Rt/Rg from the V-I characteristics of bulb: Further increase the filament
current in steps of 0.1 amp. and note the corresponding values of filament voltage for
each value of filament current. Record all these readings in table-II as shown below.
3. Calculate Rt and Rt/ Rg for each value of filament current and voltage.
TABLE: - II For V-I Characteristics of the Filament bulb
S.No.
Filament Current
Filament Voltage
Rt Ohm
I Amp.
V Volt
1.
2.
3.
4.
Rt / Rg
(b) Observations of θ and to determine the value of Planck’s constant ‘h’
4. Adjust the filament bulb at some distance ‘d’ from the solar cell on mini optical
bench.
5. Increase the filament current to such extend that the digital microammeter reads some
photo-current say mini 2 µA to 3 µA. Note this value of filament current and
photocurrent and record it in table- II as shown below.
6. Increase the filament current in steps of 0.1 amp. As in previous case and note the
corresponding photo-current for each value of filament current. Record these readings
in table- III.
7. Note the value of Rt/ Rg for each value of filament current from table-II and record
these readings in table -III.
8. Note the corresponding temperatures for each value of Rt/ Rg from graph no I or
table-IV for Rt/ Rg Vs Temp T oK for tungsten.
9. Calculate log and 1/T oK.
10. Plot graph between log Vs 1/ToK and find the slope of the curve.
11. Repeat the experiment at different value of ‘d’ between the bulb and solar cell.
-5Table-III For θ
For distance between the filament bulb and solar cell d =
cm
Wavelength
 = 6000 A0
S.No. Filament Filament CorresPhotoToK
1
log
x10  4
Current voltage
ponding
current
from
T oK
I Amp. V volt
Rt/ Rg from µA
graph
table
or
Rt/
Rg
o
graph.
Vs T K
1.
2.
3.
4.
Calculations:
From equation (7)
h  2.303
0 K log 
c
x
T oK
x10 4
Where o= 6000 A0 mean wavelength of light
k= 1.38 x 10-16 erg/deg. Boltzmann’s constant
c= 3x10 10 meter/sec. velocity of light
log 
1
T
= Slope of the curve.
Results:
1.
The experimentally observed values of Planck’s constant ’ h ‘= …………erg/sec.
2.
The standard value of Planck’s constant
‘ h’ =
The experimentally observed value of h is always with in 10 to 15% of the
standard value.
-6Table –IV
Relation between Rt/Rg and Temperature K for Tungsten Filament.
S. No.
01.
Temperature (K)
0273
Rt/R
0.25
02.
0300
0.29
03.
0400
0.43
04.
0500
0.55
05.
0600
0.71
06.
0700
0.85
07.
0800
0.99
08.
0900
1.15
09.
1000
1.29
10.
1100
1.45
11.
1200
1.61
12.
1300
1.79
13.
1400
1.95
14.
1500
2.11
15.
1600
2.30
16.
1700
2.46
17.
1800
2.65
18.
1900
2.85
19.
2000
3.05
20.
2100
3.26
21.
2200
3.46
22.
2300
3.66
23.
2400
3.85