A. Millikan, although best known for his "oil-drop experiment," which measured the charge of an electron, also performed pioneering research on the photoelectric effect. In experiments on lithium, for example, Millikan observed a maximum kinetic energy of $0.550 \mathrm{~eV}$ when electrons were ejected with $433.9-\mathrm{nm}$ light. When light of $253.5 \mathrm{~nm}$ was used, he observed a maximum kinetic energy of $2.57 \mathrm{~eV}$. (a) What is the work function, $W_{0}$, for lithium, as determined from Millikan's results? (b) What maximum kinetic energy do you expect Millikan found when he used light with a wavelength of $365.0 \mathrm{~nm}$ ?

Fireflies are often said to give off "cold light." Given that the peak in a firefly's radiation occurs at about $5.4 \times 10^{14} \mathrm{~Hz}$, determine the temperature of a blackbody that would have the same peak frequency. From your result, would you say that firefly radiation is well approximated by blackbody radiation? Explain.

Why can an electron microscope resolve smaller objects than a light microscope?

An electron moving with a speed of $2.1 \times 10^{6} \mathrm{~m} / \mathrm{s}$ has the same momentum as a photon. Find (a) the de Broglie wavelength of the electron and (b) the wavelength of the photon.

Light with a frequency of $1.14 \times 10^{15} \mathrm{~Hz}$ ejects electrons from the surface of sodium, which has a work function of $2.28 \mathrm{~eV}$. What is the minimum de Broglie wavelength of the ejected electrons?

Lunar Ranging Experiment At the Apache Point Observatory in New Mexico, laser pulses of $532-\mathrm{nm}$ light containing $0.115 \mathrm{~J}$ of energy are aimed at the Moon. (a) How many photons of light are in each pulse? (b) The laser pulse spreads out to a spot of radius $2.0 \mathrm{~km}$ at the Moon's surface. The retroreflector mirror array left by the Apollo $15$ astronauts has an area of about $0.60 \mathrm{~m}^{2}$. How many laser photons hit the mirror array? (c) The reflected light spreads out to a spot of radius $2.0 \mathrm{~km}$ back at the Apache Point Observatory. How many reflected photons are collected by the $3.5-\mathrm{m}$-diameter telescope? (In practice only about $0.25$ photon per pulse is collected.)

A microwave oven can heat $205 \mathrm{~mL}$ of water from $20.0^{\circ} \mathrm{C}$ to $90.0^{\circ} \mathrm{C}$ in $2.00 \mathrm{~min}$. If the wavelength of the microwaves is $\lambda=12.2 \mathrm{~cm}$, how many photons were absorbed by the water? (Assume no loss of heat by the water.)

The latent heat for converting ice at $0^{\circ} \mathrm{C}$ to water at $0{ }^{\circ} \mathrm{C}$ is $80.0 \mathrm{kcal} / \mathrm{kg}$. How many molecules of $\mathrm{H}_2 \mathrm{O}$ can one photon, of frequency $6.0 \times 10^{14} \mathrm{~Hz}$, convert from ice to water?

The latent heat for converting ice at $0^{\circ} \mathrm{C}$ to water at $0{ }^{\circ} \mathrm{C}$ is $80.0 \mathrm{kcal} / \mathrm{kg}$. How many photons of frequency $6.0 \times 10^{14} \mathrm{~Hz}$ must be absorbed by a $1.0 \mathrm{~kg}$ block of ice at $0^{\circ} \mathrm{C}$ to melt it to water at $0^{\circ} \mathrm{C}$ ?

You want to construct a photocell that works with visible light. Three materials are readily available: aluminum $\left(W_{0}=4.08 \mathrm{~eV}\right)$, lead $\left(W_{0}=4.25 \mathrm{~eV}\right)$, and cesium $\left(W_{0}=2.14 \mathrm{~eV}\right)$. Which material(s) would be suitable?

Studies have shown that some people can detect $545 \mathrm{~nm}$ light with as few as 100 photons entering the eye per second. What is the power delivered by such a beam of light?

An electron that is accelerated from rest through a potential difference $V_0$ has a de Broglie wavelength $\lambda_0$. What potential difference will double the electron's wavelength? (Express your answer in terms of $V_0$.)

Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the frequency of the light is increased while the intensity is held constant, describe whether the following quantities increases, decreases, or stays the same: the electric current in the phototube.

Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the frequency of the light is increased while the intensity is held constant, describe whether the following quantities increases, decreases, or stays the same: the number of electrons ejected per second.