Physics Group: Mei Mei Chan,

Travis Christolear, David Lao,

Alex Pearson, Chris Perez,

Luke Singleton, Colin Smith,

Po Tsui

Faculty Advisors: Vladimir

Gasparyan, Thomas Meyer

FOUR MEASUREMENTS

OF PLANCKS CONSTANT

Plancks constant h is fundamental to the quantum theory of matter and radiation. This constant, introduced by Planck in 1900, revolutionized the world of modern

physics. It appears in Einsteins explanation of the photoelectric effect, in Bohrs model for the hydrogen atom, and Schrdingers equation among others. We

performed four experiments in which we obtain experimental values for h.

electrons are emitted when light is incident

on a metal surface. This is known as the

photoelectric effect 1).

In 1905 Albert Einstein applied Planck's

theory of the quantization of light and

explained the photoelectric effect in terms

of the quantum model using:

E h f = KEmax + .

E is the energy supplied by the quantum of

light or a photon, KEmax is the maximum

kinetic

energy

of

the

emitted

photoelectrons, and is the energy

needed to remove them from the surface of

the material (the work function).

Electrons can be emitted from the surface

of a material, in this case a metal, when

they are bombarded by photons with an

energy greater than the work function of

the metal. In the h/e experiment, photons

with energy hf are incident on the cathode

of a vacuum tube.

The electrons in the cathode use a

minimum of their energy to escape,

leaving the surface with a maximum energy

of KEmax. By applying a reverse potential V

between the anode and cathode, the

photoelectric

current

can

be

stopped. KEmax can then be determined by

measuring the minimum reverse potential

needed to bring the photoelectric current to

zero.

Thus, Einstein's relationship becomes hf =

Ve + , or

V = (h/e) f - ( /e)

Eq. 1

A plot of V versus f for different frequencies

of light will yield a linear plot with a slope

(h/e) and a V intercept of (- /e). Since

intensity of the light does not affect the

kinetic energy of the photoelectrons, the

stopping potential remains constant for

eferences:

different

intensities to

of Modern

light and

because

the

) Anderson,

Introduction

Physics,

Saunders

stopping

potential

depends

only on

the

) Hecht,

Physics:

Algebra/Trig,

Brooks/Cole

(1998)

frequency, it is confirmed that the photon

The Balmer Series

Fig. 3

Fig. 1

Filter Experiment

S t o p p in g P o t e n t ia l ( V )

Theory: Hertz discovered in 1887 that

The Photoelectric

Effect

Theory: In the 19th century it was discovered that

hot materials and gases emit light of characteristic

wavelengths. It was not until 1885 that a Swiss high

school teacher, Johann Balmer, found an empirical

relationship, called the Balmer formula for hydrogen

2)

, for the wavelength

= RH ( - )

Eq. 2

Stopping Potential vs. Frequency

2.5

Fits

f(x) = 0.4 x 0.4

2

where n = 3, 4, 5 ... and the Rydberg constant RH has

the value 1.097 107 m-1.

Nils Bohr gave a theoretical explanation for this

formula in 1913, based on the earlier discovery by

Max Planck, that light is quantized. The Bohr model of

the hydrogen atom2) yields a formula for RH

f(x) = 0.41 x 1.33

RH = 2 m k2 e4 2 / h3 c

f(x) = 0.44 x 1.49

1.5

LED

1

Linea

r

(LED)

0.5

0

4

4.5

5

5.5

6

6.5

7

7.5

8

8.5

Frequency ( 1014 Hz)Fig.

Fig. 2 LED experiment

4

Experimental Methods and Results: In the design of photoelectric

effect experiments we need a source of light of various wavelengths. In two of

these experiments performed, we utilized color filters to eradiate a metallic

surface with monochromatic light (Fig. 1). We should point out that the two filter

experiments differ only in the equipment used.

Alternatively, in a third

experiment, we use light emitting diodes (LEDs) to provide a source of

monochromatic photons (Fig. 2). In all three experiments we apply an electric

potential between the anode and cathode, as shown in Fig. 3. The resulting

electric field between the anode and cathode opposes the energy of the emitted

photoelectrons. The voltage required to stop the current flow is proportional to

the energy of the photoelectrons.

In Fig. 4 we have plotted the stopping potential for various sources of light vs. the

frequency of the incident light. We fitted the data to Eq. 1. In the case of the

two filter experiments we arbitrarily set to zero, which allows for a more

optically pleasing comparison of the three curves. Using the value of e = 1.602 x

-19

10

C, we obtain the three values of h from the slopes of the three lines.

Fig. 5

hfilter1 = 6.49 x 10-34 Jsec;

hfilter2 = 6.98 x 10-34 Jsec;

hLED = 6.52 x 10-34 Jsec

(1982)

Fig. 6

Eq. 3

where m is the mass of the electron, e is its electric

charge, c is the speed of light and h is Planck's

constant. k is the Coulomb constant . We have

measured e and c in separate experiments during this

year's REVS-UP program. In this experiment we

measure RH, which allows us to compute h.

Experiment and Results.: We used a standard

optical spectroscope (see Fig. 5), in which light from a

hydrogen lamp is passed through a 300 lines/mm

grating. The wavelengths of the characteristic lines of

hydrogen (see. Fig. 6) are measured by determining

the angle of diffraction for each line with a telescope.

The relationship between wavelength and the

angle is given by d sin = m, where d is the

spacing between the lines of the grating and m = 1,

2, 3 ... We obtain

1 = 647 nm (red); 2 = 475.5 nm (green); 3 = 424

nm (blue)

where the subscript of refers to the value of n in the

Balmer formula (Eq. 1). These results yield an average

value of RH = 1.124 107 m-1. Substituting the

values for m, k, e, and c into Eq. 2 we determine the

value of h = 6.57 10-34 J sec, in good agreement

Conclusions:

We

have

measured

Planck's

with measurements of h obtained using the

constant

in

four

separate

experiments.

We

use

the

photoelectric effect and the accepted value of h.

photoelectric effect to determine h in three different

experiments, each with different equipment, and,

using a totally different method, we also measure h in

a spectroscopic experiment. All experiment are in

good agreement with the accepted value of h = 6.626

-34