Ch.6 - Electronic Structure of Atoms

Problem 88a

Chapter 6, Problem 88a

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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Textbook Question

In January 2006, the New Horizons space probe was launched from Earth with the mission to perform a flyby study of Pluto. The arrival at the dwarf planet was estimated to happen after nine years, in 2015. The distance between Earth and Pluto varies depending on the location of the planets in their orbits, but at their closest, the distance is 4.2 billion kilometers (2.6 billion miles). Calculate the minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth.

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Textbook Question

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 DVD player has an output wavelength of 650 nm and a power level of 5.0 mW. How many photons strike the DVD surface during the playing of a DVD 90 minutes in length?

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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?

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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?

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Textbook Question

Consider a transition in which the electron of a hydrogen atom is excited from n = 1 to n = ∞. (c) What will occur if light with a shorter wavelength than that in part (b) is used to excite the hydrogen atom?