If the maximum kinetic energy of emitted photoelectrons

• Since energy is always conserved, the energy of an incident photon is equal to: The work function + the maximum kinetic energy of the photoelectron • The energy within a photon is equal to hf • This energy is transferred to the electron to release it from a material (the work function) and the remaining amount is given as kinetic energy to the emitted photoelectron • This equation is known as the photoelectric equation: E = hf = Φ + ½ mv 2 max • Where: • h = Planck's constant (J s) • f = the frequency of the incident radiation (Hz) • Φ = the work function of the material (J) • ½ mv 2 max = E k(max) = the maximum kinetic energy of the photoelectrons (J) • This equation demonstrates: • If the incident photons do not have a high enough frequency and energy to overcome the work function (Φ), then no electrons will be emitted • hf 0 = Φ, where f 0 = threshold frequency, photoelectric emission only just occurs • E k(max) depends only on the frequency of the incident photon, and not the intensity of the radiation • The majority of photoelectrons will have kinetic energies less than E k(max) Step 1: Write out the photoelectric equation and rearrange to fit the equation of a straight line E = hf = Φ + ½ mv 2 max → E k(max) = hf - Φ y = mx + c Step 2: Identify the threshold frequency from the x-axis of the graph When E k = 0, f = f 0 Therefore, the threshold frequency is f 0 = 4 × 10 14 Hz Kinetic Energy & Intensity • The kinetic energy of the photoelectrons is independent of the ...

\( \newcommand\): Millikan's photoelectric experiment. (left) High light intensity increase photocurrent (number of collected photoelectrons). (right) Low light intensity has reduced photocurrent. However, the kinetic energy of the ejected electrons is independent of incident light intensity. (Michael Fowler). Lenard's Experimental Results (Intensity Dependence) In 1902, Hertz's student, Philipp Lenard, studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination (Figure \(\PageIndex\)). Millikan's Experimental Results (Wavelength Dependence) The American experimental physicist Robert Millikan followed up on Lenard's experiments and using a powerful arc lamp, he was able to generate sufficient light intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color - the shorter wavelength, higher frequency light caused electrons to be ejected with more energy (Figures \(\PageIndex\): Schematic drawings showing the characteristics of the photoelectric effect from Lenard's and Millikan's experiments. (A) The kinetic energy of any single emitted electron increases line...

Created By : Reviewed By : Last Updated : Apr 10, 2023 Use the free Photoelectric Effect Calculator to find the kinetic energy of ejected electrons. All you need to do is provide incident light frequency, threshold frequency and press the calculate button to avail the result in a fraction of seconds. Photoelectric Effect Calculator: Do you know that calculating the maximum kinetic energy is very easy by using our free calculator? It produces the maximum kinetic energy of ejected electrons in a less amount of time. Check the simple step by step process to evaluate the photoelectric effect of the electrons and formulas in the below sections. Also, see the solved examples for a clear idea about the concept. The following are the detailed steps on how to calculate the photoelectric effect. Go through these steps and follow to obtain the result. • Make a note of the incident light frequency and threshold frequency. • Subtract the frequency of the incident photon from the threshold frequency. • Multiply it with the planck constant to check the kinetic energy of electrons. When incident light falls on a metal surface, then it emits electrons which are called photoelectrons and the process is called the photoelectric effect. The emission of photoelectrons and kinetic energy depends on the light frequency that is incident on it. The formula to calculate the maximum kinetic energy of the emitted electrons is KE = h(f - f0) f = (KE/h) + f0 f0 = h(f - KE) Where, KE is the maximum kine...

By the end of this section, you will be able to do the following: • Describe Einstein’s explanation of the photoelectric effect • Describe how the photoelectric effect could not be explained by classical physics • Calculate the energy of a photoelectron under given conditions • Describe use of the photoelectric effect in biological applications, photoelectric devices and movie soundtracks Teacher Support The learning objectives in this section will help your students master the following standards: • (3) Scientific processes. The student uses critical thinking, scientific reasoning, and problem solving to make informed decisions within and outside the classroom. The student is expected to: • (D) : explain the impacts of the scientific contributions of a variety of historical and contemporary scientists on scientific thought and society. • (8) Science concepts. The student knows simple examples of atomic, nuclear, and quantum phenomena. The student is expected to: • (A) : describe the photoelectric effect and the dual nature of light. Section Key Terms Teacher Support [EL]Ask the students what they think the term photoelectric means. How does the term relate to its definition? When light strikes certain materials, it can eject electrons from them. This is called the photoelectric effect, meaning that light ( photo) produces electricity. One common use of the photoelectric effect is in light meters, such as those that adjust the automatic iris in various types of cameras. An...

Learning Objectives By the end of this section, you will be able to: • Describe a typical photoelectric-effect experiment. • Determine the maximum kinetic energy of photoelectrons ejected by photons of one energy or wavelength, when given the maximum kinetic energy of photoelectrons for a different photon energy or wavelength. When light strikes materials, it can eject electrons from them. This is called the photoelectric effect, meaning that light ( photo) produces electricity. One common use of the photoelectric effect is in light meters, such as those that adjust the automatic iris on various types of cameras. In a similar way, another use is in solar cells, as you probably have in your calculator or have seen on a roof top or a roadside sign. These make use of the photoelectric effect to convert light into electricity for running different devices. Figure \(\PageIndex\): Photoelectric effect. A graph of the kinetic energy of an ejected electron, \(KE_e\), versus the frequency of EM radiation impinging on a certain material. There is a threshold frequency below which no electrons are ejected, because the individual photon interacting with an individual electron has insufficient energy to break it away. Above the threshold energy, \(KE_e\), increases linearly with \(f\), consistent with \(KE_e = hf - BE\). The slope of this line is \(h\)—the data can be used to determine Planck’s constant experimentally. Einstein gave the first successful explanation of such data by prop...

When light of frequency 2.42 X 10^15 Hz is incident on a metal surface, the fastest photoelectrons are found to have a kinetic energy of 1.7eV. Find the threshold frequency of the metal. Let's explore how to use Einstein's photoelectric equation to solve such numerical on photoelectric effect. Created by Mahesh Shenoy. let's solve a problem on photoelectric effect when light of frequency 2.42 times 10 to 15 hertz is incident on a metal surface the fastest photoelectrons are found to have a kinetic energy of 1.7 electron volt find the threshold frequency of the metal how do we do this whenever i'm dealing with any question on photoelectric effect i always go back to photoelectric equation einstein's photoelectric equation because i know you can solve any problem just by understanding that equation so let's go back let's quickly recap what the einstein's photographic equation was it said if you have an electron inside a metal and you shine light on it light which is made of photons then those photons have some energy which we can call e of ph energy of photons and when the electron absorbs that energy it uses it for two things a part of it is used to overcome the work function the work function represents the minimum energy the electron needs to escape the metal and so the photon needs to at least have that much energy otherwise no photoelectric effect is going to happen so if my photon has more than enough energy then part of it is used to overcome the work function and the...