Planck Short

7/27/2019 Planck Short

1/4

Determination of Plancks constant using Wiens distribution law

Apparatus Used: Solar cell (Photo-voltaic cell- Celliniun type), Optical Filters (Blue, Green andRed), Convex Lens

Brief Theoretical Description & Formulae Used: In this experiment we make use of Wiensdistribution law for the experimental determination of Plancks constant. The Wiens law is anapproximate form of Plancks distribution formula in the high frequency (or equivalently short wave-length) limit:

u()d =8hc

5exp( hc/k B T ) d. (1)

u()d Energy per unit volume emitted by the black-body within the wavelength interval to + d,kB is the Boltzmanns constant T Absolute temperature of the black-bodyh is Plancks constant to be determined by the experiment

In the present experiment, we idealize a tungsten lament (bulb) as a perfect black body, describedby Wiens distribution law. The radiation emitted by the lament is measured by means of a photo-voltaic cell. Typically the photo-current obeys the following relationship:

I (, T ) = B exp( hc/k B T ) (2)

loge I = log e B hc

kB T (3)

We compare above equation with an equation of a straight line

y = C mx. (4)

Thus variation of log e I with 1/T comes out as a straight line, calculating slope of this allows oneto determine h.

Slope = m = hckB

(5)

Temperature of the black-body can be obtained as follows,At temperature T the relation with lament resistance is

1


2/4

RT R0 =

T T 0

1 .2

. (6)

At room temperature this relation reads:

RRR0

=T RT 0

1 .2

, (7)

here RT is resistance of the lament at temperature T R and R 0 is at T = 273K .

RDR 0

=T DT 0

1 .2

, (8)

here RD

= V D

/I D

is the draper voltage, the minimum voltage at which the lament just startsglowing and T D is draper temperature which is 800 K for tungsten.

Dividing Eq.(7) by (8) we obtain:

RR = RDT R800

1 .2

(9)

Now dividing Eq. (6) by (7)

T = T RRT RR

0 .833

. (10)

Here T R is the room temperature should be noted by room thermometer.

Figure 1: Schematic diagram of the experimental setup.

2


3/4

Procedure:

Note draper voltage and draper current from power supply.

Align the radiation source (light bulb), convex lens, lter and the radiation detector on theoptical bench. In this one rst bring all the components namely bulb, lens, lter and detector(solar cell) at the same height.

Next we focus radiation coming from the bulb in such a way that the maximum amount of light passes through lens and lter.

After xing the lter, we adjust the lens and solar cell in such way that the maximum amountof radiation in received by the center of the black strip on the detector.

We connect digital multimeter across the detector and use in ammeter mode (Range 2000 A).

We keep changing the voltage ( V T ) across the lament and note corresponding current ( I T )and I

Observation Table: RD = T R = K

Wavelength = A

S. No. V T (Volt) I T (Ampere) I ( Amp) RT = V T /I T T = T R R T R R0 .833

1/T loge I

1.

2.

3.

4.

Above set of observations should be taken for three wavelengths by replacing the lter.

3


4/4

Figure 2: Variation of log e I with 1 /T

Calculations: From the plot log e I versus I/T the slope is calculated as

Slope =log e I (1 /T )

(11)

Comparing Eq. (5) with (11) the value of Planck constant can be calculated as:

h = Slope kB

c

Result:

Standard Value: h = 6 .626 10 34 Joule-sec

% Error:

%Error =|Standard Value Experimental Value |

Standard Value 100 (12)

Precautions & Sources of Errors:

1. Special care should be taken while measuring the V T , particulary the draper voltage.

2. The bulb should be connected with power supply with thick wires so the resistance of the of the wires do not contribute in the RT and RD .

3. Radiation from the bulb should be properly focused.

4

Documents

Planck Short