Dualisme Cahaya Sebagai Gelombang dan Partikel Wave Properties Light intensity = 𝐼∝ 𝐸 2 Particle Properties Light intensity: 𝐼=𝑁ℎ𝑓 Fisika Modern

Quantum Theory of Light Under a constant frequency, the smallest energy unit of light is quantized. For one photon 𝐸=ℎ𝑓= ℎ𝑐 𝜆 For N photon 𝐸=𝑁ℎ𝑓 Fisika Modern

Spectrum of electromagnetic radiation Free electrons in resonance Nucleus Transition of bound electrons in atoms Fisika Modern

1.3.2 Photoelectric effect http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm Fisika Modern

Photoelectric effect applet Photoelectric effect applet Fisika Modern

Observations Monochromatic light is incident to one of the electrodes made by a particular metal. The induced current called photocurrent is collected. If V is fixed, there exists a threshold frequency o, below which there is no photocurrent. Different electrode materials have threshold frequency o Fisika Modern

Observations The photocurrent is constant above the threshold frequency under a constant illumination, regardless of the frequency. The photocurrent is proportional with the intensity. The energy of electron is proportional with the frequency. For a particular electrode and frequency of light, a stopping voltage Vs exists. No photocurrent can be collected regardless of the intensity of light. There is no measurable tie lag between the illumination of light and the release of photoelectrons. (10-9s) Fisika Modern

Graphical presentations  o Energy of photoelectrons is proportional to the frequency; Existence of threshold frequency Fisika Modern

Photocurrent is proportional to light intensity Fisika Modern

Different frequency of light has different stopping voltage Fisika Modern

Stopping voltage varies with electrode material for the same frequency increases with frequency of light for the same electrode Fisika Modern

Einstein’s interpretation Under a constant frequency, the smallest energy unit of light is quantized. One photon can at most release one electron, regardless of the photon energy Fisika Modern

where K is the kinetic energy of the photoelectron Work Function, W– the minimum energy for electron to escape from the metal surface where K is the kinetic energy of the photoelectron Photocurrent where  is the quantum efficiency, n number of photons striking to the electrode per second, q electron charge Fisika Modern

Where A is the area of the electrode exposed to light. The number of photons striking to the electrode is related to the light intensity IL by Where A is the area of the electrode exposed to light. Fisika Modern

Threshold frequency When K = 0, there is no photoelectrons. The frequency reaches the threshold frequency, i.e. Fisika Modern

Stopping voltage The reverse biasing voltage: where the photoelectrode is positively biased and the other negatively biased. When the biasing voltage increases from zero, the photocurrent decreases. At V  VS, IP = 0 Fisika Modern

Stopping voltage The physical meaning is that the potential difference barrier is decelerating the electron, and finally consumes all its kinetic energy. Thus, the stopping voltage gives us a tool to determine the kinetic energy, mgh qVS K Fisika Modern

Stopping voltage against frequency Fisika Modern

Hitung energi kinetik elektron yang dilepas oleh elektroda tersebut. Example: Cahaya ultraviolet dengan panjang gelombang 350 nm dan intensitas 1 W/ m 2 mengenai permukaan elektroda yang “work function” nya 2.2 eV. Hitung energi kinetik elektron yang dilepas oleh elektroda tersebut. Jika 1% dari photon yang datang diubah menjadi fotoelektron, berapa jumlah elektron yang dilepas per detik jika luas permukaan 1 c m 2 Diketahui konstanta Planck =6.626x 10 −34 Js= 4.136x 10 −15 eVs Fisika Modern

Failure of classical theory In 1902, Philipp Eduard Anton von Lenard observed that the energy of the emitted electrons increased with the frequency of the light. This was at odds with James Clerk Maxwell's wave theory of light, which predicted that the energy would be proportional to the intensity of the radiation. Fisika Modern

Within the experimental accuracy, (about 10-9 second), there is no time delay for the emission of photoelectrons. In terms of wave theory, the energy is uniformly distributed across its wavefront. A period of time is required to accumulate enough energy for the release of electrons. Fisika Modern

Inconsistency of Classical wave theory and experiment Fisika Modern

1.3.1 What is blackbody? Under thermal equilibrium, an object of a finite temperature emit radiation (supposed to be EM wave). It is found that an object that absorbs more also emits more radiation. A perfect absorber is an object with black surface that must of the incident energy is absorbed. It is also expected to be a perfect radiator. Consequently, a blackbody is a perfect radiation. Fisika Modern

Phenomena for a blackbody Temperature-dependence emission spectrum. Reciprocal relation between wavelength at the peak intensity max and ambient temperature T Inconsistency between observed spectrum and the prediction from classical theory (Reyleigh and Jeans) A model suggested by Planck (quanta of light energy) Fisika Modern

Temperature dependence of emission spectrum http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm http://surendranath.tripod.com/AppletsJ2.html Fisika Modern

Classic: Rayleigh – Jeans Formula 𝐸 = 𝑘 𝐵 𝑇 Total Energy in the cavity with frequency interval between v and v+dv 𝑢 𝑣 𝑑𝑣= 𝐸 𝐺 𝑣 𝑑𝑣= 8𝜋 𝑘 𝐵 𝑇 𝑐 3 𝑣 2 𝑑𝑣 Planck Radiation 𝐸 = ℎ𝑣 exp ℎ𝑣 𝑘 𝐵 𝑇 −1 𝑢 𝑣 𝑑𝑣= 𝐸 𝐺 𝑣 𝑑𝑣= 8𝜋ℎ 𝑐 3 𝑣 3 exp ℎ𝑣 𝑘 𝐵 𝑇 −1 𝑑𝑣 Fisika Modern

Inconsistency of Classical wave theory and experiment Fisika Modern

Blackbody radiation – Stefan’s Law An object having a surface temperature T will emit radiation power P which is proportional to the surface area A of the object and to the fourth power of the temperature. s is the Setfan’s constant and is equal to 5.67 x 10-8 Wm-2K-4(Jm-2s-1K-4) e is the emissivity of the object and is Fisika Modern

Stefan ‘s law The total power (area below a constant temperature curve P) Fisika Modern

Wein displacement Law Fisika Modern

-Hitung panjang gelombang yang dipancarkan tubuh anda - Berapa energi yang dipancarkan oleh tubuh anda? Fisika Modern

Blackbody radiation and ultra-violet catastrophe as we do the integration Blackbody radiation and ultra-violet catastrophe From Maxwell E.M. theory we know that a dipole oscillating with frequency n will on average emits energy r(n) r(n) = const. n2 where is the average energy of the oscillating dipole. Rayleigh - Jean's Law Maxwell-Boltzman distribution gives the energy state number density N(E) at energy E as total number of possible energy state and Total energy Hence the average energy: r(n) Rayleigh-Jeans Blackbody radiation UV catastrophe n Fisika Modern

This is called UV catastrophe. Ultra-violet catastrophe This result is in fact well known from kinetic theory where the energy of vibrational degree of freedom The energy of rotational / bending degree of freedom So now we have r(n) = Const. n2T Rayleigh-Jeans Law describes the beginning part of the blackbody radiation correctly at low frequency (long wavelength) but it obviously wrong at high n. As n increases r(n) increases without limit, i.e. At , as we do the integration , r(n), the radiate energy goes to infinity! This is called UV catastrophe. Fisika Modern

Planck's derivation of blackbody radiation Rayleigh - Jean's Law: This integration assume continuous distribution of energy, i.e. the oscillator can take up any value. Plank made the hypothesis that the oscillator will only take up discrete energies 0, E0, 2E0, 3E0, .....etc. the average energy is obtained from a summation instead of integration. Let Fisika Modern

Blackbody radiation http://surendranath.tripod.com/Applets.html Fisika Modern

Conclusion Rayleigh – Jeans ‘s derivation is only valid at long wavelengths (low frequencies) and fails at short wavelength. Planck made an assumption: energy emitted from the radiator at a frequency , E = nh, where n and integer, h the Planck constant (energy is discretized) Implication: classical theory predicts energy is continuous Fisika Modern