Photoelectric Effect Explained: Unlocking Quantum Physics

Light has been proven to be both a wave and a particle, featuring a particle character known as a photon. In addition, this photon is a packet of wave or radiation that has diverse energy spectrums. Therefore, when these photons come into contact with the surface of an object, electrons are emancipated.

The photoelectric effect refers to the discharge of electrons when light falls on the surface of the object. As electrons pass across the surface, charge accumulates, inducing the electric current. The entire course of transforming electromagnetic radiation into electricity is known as the photoelectric effect, and thus released electrons are known as photoelectrons.

Additionally, the induced current is identified as photoelectric current. This experiment initially demonstrated the particle nature of light.

Historical Background

In 1887, while researching spark discharges caused by potential differences between two metal surfaces, Hertz detected a main spark emanating from one surface. This resulted in an additional spark on the opposing side. To expel the distracting light and make the subsequent flare easier to observe, he put up a protective barrier around it. He was fascinated by how this led to the diminution of the tertiary flash. Next, he discovered that the consequence was triggered via the portion of the barrier that was between the two flashes. There was not an electrostatic action considering there was no discernible difference regarding the conductivity of the surface.

Hertz got underway to think that it may be related to the light emitted by the main flame. In an astonishing sequence of investigations, he demonstrated that light can generate ignition. As an instance, he set the distance among the metal surfaces to a point where the sparks no longer evolved. He then lit the surfaces with an adjacent electric beam. The light flares popped up again. Thus, Hertz spotted the photoeffect while studying the wave character of light.

In 1902, Philip Lenard investigated the photoeffect employing a carbon arc flame as the lighting source. He adjusted the intensity of the beam by an extent of -1000. He discovered that electron energy is not reliant on the brightness of light. The relationship between photoelectron energy and light frequency was not fully articulated.

The traditional theory of mechanics is centered on Newton’s principles of motion, which rely exclusively on absolute mass, absolute space, and absolute time and fail to address the motion of the body at non-relativistic speeds. Classical theory could not explain the emergence of refine lines in the emission and absorption of atomic spectra. It could not explain how energy gets transmitted in black body radiation. Planck reconciled the disparity by introducing discrete energy packets of radiation.

Following the advent of Planck’s quantum theory of radiation, Einstein rethought his well-`known mass-energy equivalence relationship and got going through it. In 1905, he put out a publication on the quantum theory that addressed the photoelectric effect. Einstein gave a straightforward account for the photoelectric phenomenon using his hermeneutic strategy. As per the idea a light photon transmits all of its energy to a single electron. Also, the energy transmission by one photon remains unaltered by the existence of another photon. He also noticed that an expelled electron frequently gives up energy prior to hitting the target, independent of the intensity of the photon.

Classical Wave Theory Predictions

According to classical wave theory, light is an electromagnetic wave that may be characterized in terms of color and luminosity. The intensity of light corresponds to the square of the wave’s amplitude. The wavelength of light is proportional to its frequency. It further explains that the energy of a wave is proportional to its intensity rather than its color. To gain insight into the photoelectric effect, scientists proposed that the arriving light wave’s fluctuating electric field heated and vibrated the electrons, finally releasing them off the material surface.

Pursuant to the classical illustration of light as a wave, the momentum of released electrons rises with wave amplitude. Furthermore, as the frequency of light increases, so should the pace of electron ejection that is proportional to the electric current. Thus, experiments were performed with the projection of higher-amplitude light to produce photoelectrons with higher kinetic energy. The electric current was also anticipated to increase while raising the frequency, keeping constant amplitude. However, the results were absolutely unforeseen.

The kinetic energy of electrons rose with frequency, whereas the electric current remained constant. In contrast, electric current rose with increasing light amplitude, yet kinetic energy remained unchanged. Thus, a novel framework was put forward for the comprehensive characterization of light.

Einstein’s Quantum Explanation

As stated by Einstein, electromagnetic radiations tend to interact like particles with specific momentum, and these particles of radiation have been termed as photons. A photon’s energy may be determined using Planck’s relation:

E = hf (Equation 1)

Where h = 6.626Χ 10^-34 Js is known as Planck’s constant and f is the frequency of photon.

Planck’s equation implies that the energy of a photon corresponds to the frequency of light. 

Work function and Threshold Frequency

The work function refers to the minimal energy necessary to expel electrons from a material’s surface which is denoted as φ. The alkali metals possess minuscule work functions, making them suitable for photoelectricity production whereas insulators, such as wood and plastic, have substantial work functions, making photoelectricity production unattainable. The relation for work function is given by Planck as

φ = hf₀ (Equation 2)

Here f₀ refers to the threshold frequency. The threshold frequency is the bare minimum frequency of light that arrives, necessary to expel electrons from a material’s surface. Threshold energy corresponds to the work function. The other term is the threshold wavelength which means the longest wavelength of incoming light capable of expelling electrons from a material’s surface. It’s indicated by λ₀. The relation of threshold frequency and threshold wavelength is denoted as

f₀ = c/λ₀ (c being the speed of light 3 Χ 10⁸ ms^-1) (Equation 3)

Also, work function corresponds to threshold wavelength as,

φ = f₀c/λ₀ (Equation 4)

Photoelectric Equation

The frequency association might be established by applying the law of conservation of energy. In order for electrons to exit a metal with a work function φ, հf must be greater than the work function (հν > φ). The total energy of the arriving photon E_p has to exceed the kinetic energy of the released electron E_e along with the energy required to free the electron from the metal.

E_e = E_p – φ (Equation 5)

The integer value of φ differs depending on the metal.

Now expressing the photon’s energy in terms of its frequency as

E_e = hf – φ (Equation 6)

Einstein’s photoelectric phenomenon implies that incoming photons transmit energy in two forms. (a) Some energy is utilized to expel electrons from atoms (to provide work function), and (b) the surplus energy is transmitted as photoelectron kinetic energy. This kinetic energy increases proportionally with v once the photon’s energy surpasses the work function φ.

As the kinetic energy of photoelectrons is expressed as 1/2mv_max², equation (6) becomes,

1/2mv_max² = hf – φ (Equation 7)

Using (2) in (7) we get,

1/2mv_max² = hf – hf₀ (1/2mv_max² ∝ hf) (Equation 8)  

Equation (8) is known as the renowned Einstein’s equation for photoelectric effect. For given λ and λ₀ as the consequent wavelength of incident frequency and threshold frequency’ equation (8) may be written as

1/2mv_max² = hc (1/λ -1/λ₀) (Equation 9)

Experimental Verifications

When the polarity of the collector and the emitter flips over and the collector has a negative potential, the produced photo-electrons have to compete against this potential at the cost of their kinetic energy to reach at the collector. Raising the negative potential of the collector to a stopping potential (Vs) will reject even the most rapid electrons. Therefore, we will have the situation,

1/2mv_max² = eV_s (Equation 10)

Hence, from (8) and (10) we get

V_s ∝ f (Equation 11)

The equation indicates a direct relationship between stopping potential and photon frequency, resulting in a linear plot. Robert A. Millikan conducted experiments to verify this assumption. . 

The experimeny was conducted, putting three photosensitive metals (Na, K, and Li) on a cylindrical wheel that could spin around an axis. This setup was stored within an evacuated glass tube equipped with a powerful electromagnet that could be utilized to move the wheel. The tube additionally included a knife N, which might’ve been used to scrape metal oxides from the surface of metal. The monochromatic light was permitted to strike various metals, and the released electrons were captured by a collector with a negative potential. The collector’s negative potential was steadily increased until it reached a maximum known as the stopping potential, which prevented even the most rapid electrons from reaching it. The incoming light frequency was increased, and the stopping potential was adjusted accordingly. The technique was repeated, using various light frequencies falling on the three metals designated on the wheel.

Plotting incident frequency and stopping potential for three metals resulted in a straight line with a negative y-intercept, yielding an equation of the form:

y= mx + (-c) (Equation 12)

From equations (8) and (10) we get,

V_s = h/e f + (-h/e f₀) (Equation 13)

which is analogous to equation (12). Hence, Einstein’s hypothesis was justified by the experiment.

Factors Affecting the Photoelectric Effect

The photoelectric effect is determined by a variety of parameters, comprising light frequency, intensity, material type, light energy, and potential difference. Electron emission is not affected by light intensity unless the frequency exceeds a certain threshold. The photoelectric effect occurs when a beam of radiation with a frequency equal to or above the threshold frequency hits the surface of matter. The photoelectric effect is not visible at frequencies below the threshold, which varies by substance. Increased light intensity leads to more photoelectrons, provided the frequency above the threshold. Increasing the amount of photoelectrons leads to higher photoelectric currents. Photoelectrons gain kinetic energy when high-energy light hits the target. When energy exceeds the threshold, photoelectric current is created.

Energy Conservation in the Photoelectric Effect

The concept of energy conservation stipulates that the energy essential to expel electrons (work function) plus any excess kinetic energy must equal the energy received by a photon. Thus,

E_max = hf – φ (Equation 14)

In photoelectric circuits, the positive potential that increases current is known as accelerating potential, whereas the highest achievable current is known as saturation current. The retarding potential whereby the photoelectric current turns zero is referred to as the cut off or stopping potential for a specific frequency of incoming light. Stopping potential may be denoted as V_s. The stopping voltage essential for blocking photoelectrons from approaching the anode is determined by

q_eV_s = hf – φ (Equation 15)

Applications of the Photoelectric Effect

Solar panels and photovoltaics

A solar cell, also known as a photovoltaic cell (PV), transforms solar energy into electricity when subjected to radiation. It’s a non-mechanical, semiconductor-powered machine. When photons contact a PV cell, they potentially bounce off it, penetrate it, or are captured by the semiconductor fabric. The employed photons provide energy for the creation of electricity. When adequate light gets caught on the semiconductor, electrons flow from its atoms.

The migration of electrons onto the front surface of the PV cell induces an increase in electrical charge between the cell’s forward and rear surfaces, leading to a potential difference analogous to a battery’s negative and positive terminals. The electrical conductors of a photovoltaic cell collect electrons. Whenever the conductors of an electrical circuit are hooked up to an electrical source, electricity circulates around them.

Photoelectric sensors and devices

The photoelectric sensor utilizes light to identify the existence or removal of a substance.  The sensor emits a light beam from its emitter, which passes to the detector’s recipient, which collects the light and powers the sensor. With respect to the sort of sensor, light can either go straight to the sensor’s receiver or to a reflector or an object before returning to the receiver. 

Significance in Quantum Mechanics

The experimental recognition of photons is a fundamental principle of quantum physics. All quantum theory approaches are based on the concept of wave-particle duality. A photon’s state cannot be detected or localized, but it may be correlated, yielding the entanglement theory, which is also used in quantum computing. The interaction of a photon with matter results in annihilation and multiplication of matter. This blends classical ideas like electric and magnetic fields with quantum physics of radiation.

In quantum electrodynamics, photons are considered as intermediates for electromagnetic forces between charged particles. The electromagnetic interaction on a huge surface creates a force that is proportional to radiation pressure. It is assumed that photons, or gauge bosonic particles, quantize and shift the force away.

Experimental Setup and Apparatus

The setup involves a mercury lamp, a lens with a monochromator, a photocell featuring a controller to adjust the stopping voltage, and a current amplifier with a zero adjustment for the photocurrent monitoring. Two additional multimeters are required for measuring the stopping voltage and the current. 

When subjected to monochromatic light, the target substance acts as an anode, emitting photoelectrons, and is known as a photoelectrode. The photoelectrons gather at the cathode, that has lesser voltage than the anode. The potential difference among the electrodes can be varied accordingly. An evacuated glass tube is used to encase the electrodes in order to prevent photoelectrons from losing kinetic energy when they collide with air molecules in the region within the electrodes.

When the target material is shielded (kept away from radiation), no current flows through this circuit as the connection is broken. However, if the material is coupled to the negative terminal of a power supply and subjected to radiation, a current is detected, being known as the photocurrent. Now assuming that the potential difference between the electrodes is reversed, ensuring the target material is coupled to the positive terminal of the source. The voltage is gradually raised. At certain inverted voltages, the photocurrent steadily fades and finally ceases to flow entirely. At a point the photocurrent absolutely diminishes which is called the stopping potential.

Limitations and Common Misconceptions

Some usual constraints and misconceptions regarding the photoelectric effect are highlighted below:

• Frequency dependence:

Electron emission is completely governed by the frequency of light (i.e. threshold frequency). Thus the misconception of increasing the intensity of light may lead an experimental error.

• Material dependence:

The work function of metal varies per substance. Thus, using materials with low work function may provide impressive results.

• Efficiency of photocells:

The photoelectric effect is employed in devices such as solar cells and photodetectors, although its conversion efficiency is poor. Certain incoming photons contain enough energy to liberate electrons or do so effectively.

Modern Developments and Research

Some of the significant areas of current study and development associated with the photoelectric effect are solar cells and plasmonics. The photon detection process is also highly precise, leading to the development of quantum computing and quantum cryptography. Laser pulses are being developed to achieve better time frame resolutions and measure real-time quantum events using the photoelectric effect. These pulses measure time in attoseconds (1 attosecond = 10^-18 seconds).

Conclusions

The photoelectric effect illustrates that photons are fragments of light. Thus, it should be viewed as a particle rather than a wave in order to obtain photon-like qualities. The work function of metal has a significant influence on photoelectron emission. Materials having a lower work function produce favorable outcomes.

References

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