In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labeled 'n0' corresponds to light with a wavelength of 542 nm. (a) What is the value of n0 in s - 1?

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Identify the given wavelength (λ) of light, which is 542 nm.

Convert the wavelength from nanometers to meters by multiplying by 10^-9.

Use the speed of light equation, c = λν, where c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength in meters, and ν is the frequency in s^-1.

Rearrange the equation to solve for the frequency (ν): ν = c / λ.

Substitute the values for c and λ into the equation to find the frequency ν.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Photoelectric Effect

The photoelectric effect refers to the phenomenon where electrons are emitted from a material (usually a metal) when it is exposed to light of sufficient frequency. This effect demonstrates the particle nature of light, as photons must have enough energy to overcome the work function of the material to eject electrons.

Frequency and Wavelength Relationship

The frequency (ν) and wavelength (λ) of electromagnetic radiation are inversely related through the equation c = νλ, where c is the speed of light. This means that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for converting the given wavelength of light into frequency for calculations.

Kinetic Energy of Ejected Electrons

The kinetic energy (KE) of ejected electrons in the photoelectric effect can be calculated using the equation KE = hν - φ, where h is Planck's constant, ν is the frequency of the incident light, and φ is the work function of the metal. This relationship highlights how the energy of the incoming photons is converted into the kinetic energy of the emitted electrons.

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The watt is the derived SI unit of power, the measure of energy per unit time: 1 W=1 J/s. A semiconductor laser in a CD player has an output wavelength of 780 nm and a power level of 0.10 mW. How many photons strike the CD surface during the playing of a CD 69 minutes in length?

Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (a) What is the end result of this transition?

Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (b) What is the wavelength of light that must be absorbed to accomplish this process?

Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (d) How are the results of parts (b) and (c) related to the plot shown in Exercise 6.88?