U Ultraviolet light with a single wavelength and with intensity 550 W / m^2 is incident normally

U Ultraviolet light with a single wavelength and with...

Key Concepts

Electric Current

In the context of the photoelectric effect, electric current is produced by the flow of photoelectrons emitted from the metal surface. Current is calculated by multiplying the number of electrons emitted per second (photoelectron emission rate) by the elementary charge. This concept links the microscopic particle behavior of electrons to the measurable macroscopic quantity of electric current.

Efficiency Considerations

No physical process is perfectly efficient. In the photoelectric effect, real metals do not convert every incident photon into an emitted electron. Factors such as surface conditions, photon absorption without electron emission, and recombination effects cause the actual current to be lower than the maximum theoretical value calculated under the assumption of 100% quantum efficiency.

Photon Flux

Photon flux refers to the number of photons incident per unit time per unit area. It can be calculated by dividing the light intensity (energy per unit area per unit time) by the energy per photon. This concept helps in determining the maximum possible rate of photoelectron emission, assuming that each photon can eject one electron.

Work Function

The work function is the minimum energy required to remove an electron from the surface of a metal. In the context of the photoelectric effect, the work function determines the threshold frequency (or wavelength) below which no electrons are emitted, regardless of the light’s intensity. It is a critical property that influences the kinetic energy of the emitted electrons.

Photoelectric Effect

This phenomenon involves the emission of electrons from a metal surface when it is exposed to electromagnetic radiation, typically ultraviolet light. It demonstrates that light behaves as particles (photons) where each photon can transfer its energy to an electron, allowing the electron to overcome the binding energy of the metal and be emitted. This effect was key in developing the quantum theory of light.

Photon Energy

Photon energy is determined by the equation E = h? or equivalently E = hc/?, where h is Planck’s constant, ? is the frequency, and ? is the wavelength of the light. This concept is crucial because it provides the energy available to eject electrons from the metal, and any excess energy above the work function appears as kinetic energy of the photoelectrons.

Transcript

00:01 So here in this question in the first part to find the maximum possible rate of photoelectron emission we can use the equation e is equals to p by r here electricity or the energy e can be calculated as h mu where h is the planck's constant and mu is the frequency of the incident light in hertz and if we rearrange these formulas we can write it as h mu is equals to p by r where r is the rate of photoelectron emission and p is the intensity of incident light and rearranging it to solve for r that is the rate of photoelectron emission this gives us p upon h mu where p is the intensity of incident light now to find the frequency of the incident light we can use the equation mu is equals to c by lambda where c is the speed of light and lambda is the wavelength of the incident light the wavelength of ultraviolet light the wavelength of uv light is typically between 10 nanometers and 400 nanometers in this case we are given that the wavelength of the incident light is a single wavelength so we can assume that it is somewhere between in the middle of that range.

01:26 So let's assume that this wavelength is 200 nanometers now converting the wavelength to meters lambda is equals to 200 nanometers and we can convert it in meters as 2 into 10 raised to the power minus 7 meters now we can plug in the values of p, h and mu into the equation to calculate the rate of photoelectron emission and this gives us r is equals to 550 watt centimeter square upon 6 .626 into 10 raised to the power minus 34 joules second, which is the next constant into 2 into 10 raised to the power 15 hertz, which is the frequency so from here r or the possible rate of photoelectron emission comes out to be 4 .1 into 10 raised to the power 25 electrons per second per centimeter square per second per centimeter square now in second part of this question in the second part to find the electric current these electrons constitute we can use the equation i is equals to nq where n is the number of electrons and q is the charge of each electron now substituting the known values the current i is equals to the number of electrons that is 4 .1 into 10 raised to the power 25 electrons per second into charge of the electron that is 1 .6 into 10 raised to the power minus 19 coulomb per electron per electron and this gives us the current as 6 .56 into 10 raised to the power minus 3 ampere now in third part of this question the third part the actual current will be less than the maximum possible current the actual current actual current is less than less than maximum possible current maximum possible current due to number of factors such as not every photon will produce a photoelectron some photoelectrons will be reabsorbed by the metal or some photoelectrons will be scattered before they reach the collector the actual current will also depend on the design of the photoelectron cell and in general the actual current will be a fraction of maximum possible current this fraction is known as the quantum efficiency of the photoelectron cell...

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