Determination of Planck's Constant - Revision history

Ist12916: /* Protocol */

2025-03-14T11:08:54Z

Protocol

Ist12916: /* In This Setup */

2022-11-22T09:11:38Z

In This Setup

Ist12916 at 09:08, 22 November 2022

2022-11-22T09:08:33Z

Ist165721: Text replacement - "\]" to ""

2015-05-24T18:47:14Z

Text replacement - "\]" to "</math>"

Ist165721: Text replacement - "\[" to " $"$

2015-05-24T18:42:20Z

Text replacement - "\[" to "<math>"

Ist128595 at 20:11, 6 November 2013

2013-11-06T20:11:38Z

Ist128595 at 18:50, 6 November 2013

2013-11-06T18:50:49Z

Ist128595 at 18:44, 6 November 2013

2013-11-06T18:44:09Z

Ist128595 at 18:25, 6 November 2013

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Ist165721 at 14:32, 29 October 2013

2013-10-29T14:32:00Z

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 </math>
-==In This Setup==
+==Photoelectric cell==
-A photoelectric cell is a device where light shines upon a metalic surface (cathode) and excites the electrons that will be collected by a concentric metalic surface (anode), as shown in the figure on the right (it is basically a semi-cilindric capacitor with very low capacity). If you connect the cathode and anode through an external circuit, you can measure the current created by the photoelectrons. In a more generic sense, the maximum kinetic energy of the electron is determined by applying a stopping potencial between the cathode and the anode to prevent electrons from reaching the anode. This way, when current no longer flows, we will know the value of the current.
+A photoelectric cell is a device where light shines upon a metallic surface (cathode) and excites the electrons that will be collected by a concentric metallic surface (anode), as shown in the figure on the right (it is basically a semi-cylindrical capacitor with very low capacity). If you connect the cathode and anode through an external circuit, you can measure the current created by the photo-electrons. In a more generic sense, the maximum kinetic energy of the electron is determined by applying a stopping potential between the cathode and the anode to prevent electrons from reaching the anode. This way, when current no longer flows, we will know the value of the current.
 [[File:Plank-celula1.png|thumb]]
-We begin by applying a voltage to the vell (approximatlly 9V, because the capacitor is discharged before starting the experiment by short-circuiting the terminals). With the cell in series with the capacitor, the latter will charge as electrons are generated in the cell. This creates an electric current through the cell. As the capacitor charges, the voltage between its terminals increases, reducing the volltage between the terminals of the cell(because \( V_{bat} = V_{Cap} + V_{cell} = constant \)). When the cell voltage reaches \( V_c = \frac{h  \nu - e  \phi}{e} \), current no longer flows and the capacitor maintains a constant voltage.
+We begin by applying a voltage to the cell (approximately 9V, because the capacitor is discharged before starting the experiment by short-circuiting the terminals). With the cell in series with the capacitor, the latter will charge as electrons are generated in the cell. This creates an electric current through the cell. As the capacitor charges, the voltage between its terminals increases, reducing the voltage between the terminals of the cell(because \( V_{bat} = V_{Cap} + V_{cell} = constant \)). When the cell voltage reaches \( V_c = \frac{h  \nu - e  \phi}{e} \), current no longer flows and the capacitor maintains a constant voltage.
 [[File:Constante de Planck.png|thumb|alt=Constante de Planck|Voltage (stopping power) vs. Maximum in the frequency of light]]
-Knowing two or more voltage values for certain frequencies, the user can do a linear regression and determine both \( \phi \) and Planck's constant. In the following graphic we can see the relation between the stopping potencial V and the light frequency for a given metal. This function is a linear function with slope = \( \frac{h}{\epsilon} \) and y-intercept = \( \phi \).
+Knowing two or more voltage values for certain frequencies, the user can do a linear regression and determine both \( \phi \) and Planck's constant. In the following graphic we can see the relation between the stopping potential V and the light frequency for a given metal. This function is a linear function with slope = \( \frac{h}{\epsilon} \) and y-intercept = \( \phi \).
 =Historical Elements=

← Older revision		Revision as of 09:08, 22 November 2022
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	=Description of the Experiment=		=Description of the Experiment=
−	The purpose of this experiment is to study the photoelectric effect and calculate Planck's constant using 5 different coloured leds and a photoelectric cell.	+	The purpose of this experiment is to study the photoelectric effect and calculate Planck's constant using 5 different coloured leds (different wave-lenghts) and a photoelectric cell.
		+
		+
		+	<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
		+	'''Links'''
		+	<div class="mw-collapsible-content">
		+
		+	*Video: Soon
		+	*Laboratory: [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/5/5 free.elab]
		+	*Control room: Planck
		+	Grade: *
		+
		+	</div>
		+	</div>

@@ Line 149: / Line 149: @@
 <math>
 E = h \nu
-\]
+</math>
 Where \( h \) is Planck's constant. The photoelectric effect is, essentially, a collision between a photon (light) and an electron (in the metal) where the former gives all its energy to the latter. Since the electron's energy is higher when in vacuum (as opposed when it's bound to the crystal structure of the metal), the electron is only freed if the photon energy is higher than the difference between the energy of the electron in vacuum and in the metal (figure 1). Thus, the electron leaves the metal with energy equal to the energy of the photon minus the amount "spent" when the electron leaves the metal:
@@ Line 155: / Line 155: @@
 <math>
 E = h \nu - e \phi
-\]
+</math>
 where \( e \) is the electron charge and \( \phi \) is the diference in ''workfunction''. As the light frequency decreases, the photons have less energy. Bellow a certain critical frequency \( \nu _0 \), no more photoelectrons are emitted. In this case, \( E_{max} = 0 \) and we can write:
@@ Line 161: / Line 161: @@
 <math>
 h \nu _0 = e \phi \quad or \quad \nu _0 = \frac{e}{h} \phi
-\]
+</math>
 ==In This Setup==

@@ Line 147: / Line 147: @@
 Einstein proposed the following explanation: light is made of photons with a given energy, proportional to frequency (\( \nu \)):
-\[
+<math>
 E = h \nu
 \]
@@ Line 153: / Line 153: @@
 Where \( h \) is Planck's constant. The photoelectric effect is, essentially, a collision between a photon (light) and an electron (in the metal) where the former gives all its energy to the latter. Since the electron's energy is higher when in vacuum (as opposed when it's bound to the crystal structure of the metal), the electron is only freed if the photon energy is higher than the difference between the energy of the electron in vacuum and in the metal (figure 1). Thus, the electron leaves the metal with energy equal to the energy of the photon minus the amount "spent" when the electron leaves the metal:
-\[
+<math>
 E = h \nu - e \phi
 \]
@@ Line 159: / Line 159: @@
 where \( e \) is the electron charge and \( \phi \) is the diference in ''workfunction''. As the light frequency decreases, the photons have less energy. Bellow a certain critical frequency \( \nu _0 \), no more photoelectrons are emitted. In this case, \( E_{max} = 0 \) and we can write:
-\[
+<math>
 h \nu _0 = e \phi \quad or \quad \nu _0 = \frac{e}{h} \phi
 \]

@@ Line 168: / Line 168: @@
 [[File:Plank-celula1.png|thumb]]
-We begin by applying a voltage to the vell (approximatlly 9V, because the capacitor is discharged before starting the experiment by short-circuiting the terminals). With the cell in series with the capacitor, the latter will charge as electrons are generated in the former. This creates an electric current through the cell. As the capacitor charges, the voltage between it's terminals increases, diminuishing the volltage between the cell's terminals (because \( V_{bat} = V_{Cap} + V_{cell} = constant \)). When the cell's voltage reaches \( V_c = \frac{h  \nu - e  \phi}{e} \), current no longer flows and the capacitor maintains a constant voltage.
+We begin by applying a voltage to the vell (approximatlly 9V, because the capacitor is discharged before starting the experiment by short-circuiting the terminals). With the cell in series with the capacitor, the latter will charge as electrons are generated in the cell. This creates an electric current through the cell. As the capacitor charges, the voltage between its terminals increases, diminuishing the volltage between the terminals of the cell(because \( V_{bat} = V_{Cap} + V_{cell} = constant \)). When the cell voltage reaches \( V_c = \frac{h  \nu - e  \phi}{e} \), current no longer flows and the capacitor maintains a constant voltage.
 [[File:Constante de Planck.png|thumb|alt=Constante de Planck|Voltage (stopping power) vs. Maximum in the frequency of light]]
-Knowing two or more voltage values for certain frequencies the user can do a linear regression and determine both \( \phi \) and Planck's constant. In the following graphic we can see the relation between the stopping potencial V and the light's frequency for a given metal. This function is a linear function with slope = \( \frac{h}{\epsilon} \) and y-intercept = \( \phi \).
+Knowing two or more voltage values for certain frequencies, the user can do a linear regression and determine both \( \phi \) and Planck's constant. In the following graphic we can see the relation between the stopping potencial V and the light frequency for a given metal. This function is a linear function with slope = \( \frac{h}{\epsilon} \) and y-intercept = \( \phi \).

@@ Line 94: / Line 94: @@
 [[File:Constante de Planck.png|thumb|alt=Planck's constant|Figure 2: Potential vs. Peaks Frequency of the spectrum ]]
-The photoelectron's kinetic energy depends only on the frequency of the incident light. If the frequency of light increases, the energy will increase.
+The  kinetic energy of the photoelectron depends only on the frequency of the incident light. If the frequency of light increases, the energy will increase.
 #Obtain the stop potentials for different colour leds.
@@ Line 129: / Line 129: @@
 =Advanced Protocol=
-# Study the photocell's charging process for different intensities.
+# Study the photocell charging process for different intensities.
-# Find the expected value for wavelength using the led spectra.
+# Find the wavelength expected value using the led spectra.
 # Use those values for a new graphical fitting and compare the results.
 # Redo the voltage vs. frequency graph, this time with error bars.
@@ Line 141: / Line 141: @@
 ==Photoelectric effect==
 The photoelectric effect happens when a metal surface is illuminated by a light with a given frequency, causing electrons to be freed.
-When a photon with energy \( E \) collides with a metal, it transfers it's energy to an electron in the crystal structure. The emission of electrons is deeply connected to the frequency of the light shone upon the surface.
+When a photon with energy \( E \) collides with a metal, it transfers its energy to an electron in the crystal structure. The emission of electrons is deeply connected to the frequency of the light shone upon the surface.
 For each metal there is a critical frequency, \( \nu _0 \). If incident radiation has frequency bellow \( \nu _0 \), then there are no emitted electrons. If the former is above the latter, then the kinetic energy of the emitted electrons is proportional to the energy of the photons.
-The light's intensity changes only the number of emitted photoelectrons, not it's energy (this goes against what is expected in the classical theory of radiation).
+The light intensity changes only the number of emitted photoelectrons, not its energy (this goes against what is expected in the classical theory of radiation).
 Einstein proposed the following explanation: light is made of photons with a given energy, proportional to frequency (\( \nu \)):
@@ Line 151: / Line 151: @@
 \]
-Where \( h \) is Planck's constant. The photoelectric effect is, essentially, a collision between a photon (light) and an electron (in the metal) where the former gives all it's energy to the latter. Since the electron's energy is higher when in vacuum (as opposed when it's bound in the metal's crystal structure), the electron is only freed if the photon's energy is higher than the difference between the electron's energy in vacuum and in the metal (figure 1). Thus, the electron leaves the metal with energy equal to the photon's energy minus the amount "spent" when the electron leaves the metal:
+Where \( h \) is Planck's constant. The photoelectric effect is, essentially, a collision between a photon (light) and an electron (in the metal) where the former gives all its energy to the latter. Since the electron's energy is higher when in vacuum (as opposed when it's bound to the crystal structure of the metal), the electron is only freed if the photon energy is higher than the difference between the energy of the electron in vacuum and in the metal (figure 1). Thus, the electron leaves the metal with energy equal to the energy of the photon minus the amount "spent" when the electron leaves the metal:
 \[
@@ Line 157: / Line 157: @@
 \]
-where \( e \) is the electron charge and \( \phi \) is the diference in ''workfunction''. As the light's frequency decreases, the photons have less energy. Bellow a certain critical frequency \( \nu _0 \), no more photoelectrons are emited. In this case, \( E_{max} = 0 \) and we can write:
+where \( e \) is the electron charge and \( \phi \) is the diference in ''workfunction''. As the light frequency decreases, the photons have less energy. Bellow a certain critical frequency \( \nu _0 \), no more photoelectrons are emitted. In this case, \( E_{max} = 0 \) and we can write:
 \[
@@ Line 164: / Line 164: @@
 ==In This Setup==
-A photoelectric cell is a device where light shines upon a metalic surface (cathode) and exites electrons that will be collected by a concentric metalic surface (anode) like what's shown in the figure on the right (it is basically a semi-cilindric capacitor with very low capacity). If we connect the cathode and anode through an external circuit we can measure the current created by the photoelectrons. In a more generic sense, the electron's maximum kinetic energy is determined by applying a stopping potencial between the cathode and the anode to prevent electrons from reaching the former. This way, when current no longer flows, we will know the the value of the current.
+A photoelectric cell is a device where light shines upon a metalic surface (cathode) and excites the electrons that will be collected by a concentric metalic surface (anode), as shown in the figure on the right (it is basically a semi-cilindric capacitor with very low capacity). If you connect the cathode and anode through an external circuit, you can measure the current created by the photoelectrons. In a more generic sense, the maximum kinetic energy of the electron is determined by applying a stopping potencial between the cathode and the anode to prevent electrons from reaching the anode. This way, when current no longer flows, we will know the value of the current.
 [[File:Plank-celula1.png|thumb]]

@@ Line 8: / Line 8: @@
 The potential between the plates of the photocell will increase with the emitted photoelectron accumulation. After reaching a certain voltage, the stopping potential will be greater than the photoelectron's kinetic energy, and these will not have enough energy to reach the second plate. This voltage will depend on the wavelength of the incident light (photon energy).
-After each experiment the photocell is connected to ground to discharge it.
+After each experiment the photocell is connected to ground to discharge.
 The leds have different efficiency, leading to different intensities for a chosen brightness. Therefore, the charging time will be different between colors.
-The graph in figure 1 shows each led's spectrum, table 1 having more details.
+The graph in figure 1 shows each led spectrum, table 1 shows more details.
-Please note that the wavelength for each led depends on the junction's temperature, and this will depend not only on room temperature, but also on the current passing through the junction. This effect (red shift) is more noticeable in warm-coloured led (green-red) than blue, so the calculation of Planck's constant will suffer a shift.
+Please note that the wavelength for each led depends on the junction temperature, and this will depend not only on room temperature, but also on the current passing through the junction. This effect (red shift) is more noticeable in warm-coloured led (green-red) than in the blue one, so the calculation of Planck's constant will suffer a shift.
 {| border="1" style="text-align: center;"
-|+ Table 1 – Led's spectrum peaks; these values should be used considering the wavelength's dispersion with 7 mA.
+|+ Table 1 – Led spectrum peaks; these values should be used considering the wavelength dispersion with 7 mA.
 |-
 !Color

← Older revision		Revision as of 14:32, 29 October 2013
Line 164:		Line 164:

	==In This Setup==		==In This Setup==
−	~~UNDER CONSTRUCTION~~.	+	A photoelectric cell is a device where light shines upon a metalic surface (cathode) and exites electrons that will be collected by a concentric metalic surface (anode) like what's shown in the figure on the right (it is basically a semi-cilindric capacitor with very low capacity). If we connect the cathode and anode through an external circuit we can measure the current created by the photoelectrons. In a more generic sense, the electron's maximum kinetic energy is determined by applying a stopping potencial between the cathode and the anode to prevent electrons from reaching the former. This way, when current no longer flows, we will know the the value of the current.
		+
		+	[[File:Plank-celula1.png\|thumb]]
		+
		+	We begin by applying a voltage to the vell (approximatlly 9V, because the capacitor is discharged before starting the experiment by short-circuiting the terminals). With the cell in series with the capacitor, the latter will charge as electrons are generated in the former. This creates an electric current through the cell. As the capacitor charges, the voltage between it's terminals increases, diminuishing the volltage between the cell's terminals (because \( V_{bat} = V_{Cap} + V_{cell} = constant \)). When the cell's voltage reaches \( V_c = \frac{h \nu - e \phi}{e} \), current no longer flows and the capacitor maintains a constant voltage.
		+
		+	[[File:Constante de Planck.png\|thumb\|alt=Constante de Planck\|Voltage (stopping power) vs. Maximum in the frequency of light]]
		+
		+	Knowing two or more voltage values for certain frequencies the user can do a linear regression and determine both \( \phi \) and Planck's constant. In the following graphic we can see the relation between the stopping potencial V and the light's frequency for a given metal. This function is a linear function with slope = \( \frac{h}{\epsilon} \) and y-intercept = \( \phi \).