Determination of Planck's constant using Photo Vacuum Tube
Planck's constant is the fundamental constant in modern physics. It relates the energy of a photon to its frequency. To determine this constant we can use Light Emitting Diodes (LED) also. Diodes today come in a variety of colors. Each color is achieved by having a slightly different semiconductor material. We can choose a number of LEDs, with different colors including Blue, Green, Red and Orange.
The experiment is based on the fact that the energy of the photon relates to its frequency as:
E = h x f
1. Take the Planck's constant Setup & fix the photo vacuum tube at particular position.
2. Connect + ive terminal of DC power supply to + ive terminal of DC voltmeter and –ive terminal of DC ammeter.
3. Now connect - ive terminal of DC power supply to - ive terminal of DC voltmeter.
4. Connect + ive terminal of DC ammeter to anode (+ ive terminal) of photo vacuum tube.
5. Connect - ive terminal of DC voltmeter to Cathode (- ive terminal) of photo vacuum tube as shown in figure below.
6. Set the range of DC voltmeter at 200 mV and Ammeter at 2 μA.
7. Connect the mains cord and switch on the power supply and light source.
8. Now you can observe some value of current on ammeter.
9. Now first insert the blue color filter in front of photo vacuum tube.
Note: After inserting filter, if you are not getting current properly then slide the photo vacuum tube towards light source till the getting some current.
10. Switch on the DC power supply.
11. Now vary the DC voltage slowly by variable resistance pot and see the value of current. It will be decreases as the increase of voltage.
12. When the current becomes zero, note the value of applied voltage by DC voltmeter. This is stopping potential for blue color.
13. Now switch off the DC power supply.
14. Again repeat the same procedure for different colors of filters at same distance.
15. Note down all the values in observation table given below.
Colour | Wavelength (in nm ) | Frequency ν = c/ λ (in Hz x 10^{14}) | Stopping potential Vo |
16. Plot the graph between Frequency on X- axis and stopping potential on Y- axis.
V = ν (h/e) - W/e
Where, V= stopping potential
ν = Frequency of light corresponding to the wavelength
W = work function of the metal in the tube
h = Planck’s constant
e = charge on electron = 1.6x 10-19 coulomb.
This follows the normal straight line formula of: y = ax + b
So, Slope = h/e Or h= Slope x e
h =........... Joule Sec.
The intercept on the Y axis will be -W/e
Calculation of Percentage Error
Standard value of plank‟s constant = 6.62 X 10^{-34} joule seconds
Colour | Wavelength (in nm ) | Frequency ν = c/ λ (in Hz x 10^{14}) | Stopping potential |
Blue | 475 | 6.315 | 0.813 |
Green | 510 | 5.882 | 0.592 |
Yellow | 570 | 5.263 | 0.408 |
Orange | 590 | 5.084 | 0.256 |
Red | 650 | 4.615 | 0.143 |
The straight line can be obtained by using any graph analysis software like MS Excel, Origin or any other spread sheet software.
From above graph
Slope = 3.94 x 10^{-15}............... (1)
Extrapolating the straight line
h / e = Y intercept / X intercept = 1.6 / 4.1 x 10^{14}= 3.90 x 10^{-15}
Slope of the straight line gives the ratio, h / e
Slope = 3.90 x 10^{-15} .................... (2)
Taking average of Equn (1) & (2)
h / e = 3.92 x 10^{-15}
Slope = h/e
So that,
h = ( Slope x e ) = (h/e) x e
And e = elementary charge = 1.6 x 10^{-19}
Substituting the value of slope in formula h= Slope x e
h = ( 3.92 x 10^{-15}) x ( 1.6 x 10^{-19})
= 6.27 x 10^{-34} Js
Percentage Error = 6.62 - 6.67 / 6.62 = 5.28%
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