A microwave operates at 250. W. Assuming that the waves emerge from a point source emitter on one side of the oven, how long does it take to melt an ice cube $2.00 \mathrm{~cm}$ on a side that is $10.0 \mathrm{~cm}$ away from the emitter if $10.0 \%$ of the photons are absorbed by the cube? How many photons of wavelength $10.0 \mathrm{~cm}$ hit the ice cube per second? Assume a cube density of $0.960 \mathrm{~g} / \mathrm{cm}^3$.

Quantum theory says that electromagnetic waves actually consist of discrete packets-photons-each with en$\operatorname{ergy} E=\hbar \omega$, where $\hbar=1.054573 \cdot 10^{-34} \mathrm{Js}$ is Planck's reduced constant and $\omega$ is the angular frequency of the wave. a) Estimate the momentum of a photon. b) Estimate the angular momentum of a photon. Photons are circularly polarized; that is, they are described by a superposition of two plane-polarized waves with equal field amplitudes, equal frequencies, and perpendicular polarizations, one-quarter of a cycle ( $90^{\circ}$ or $\left.\pi / 2 \mathrm{rad}\right)$ out of phase, so the electric and magnetic field vectors at any fixed point rotate in a circle with the angular frequency of the waves. It can be shown that a circularly polarized wave of energy $U$ and angular frequency $\omega$ has an angular momentum of magnitude $L=U / \omega$. (The direction of the angular momentum is given by the thumb of the right hand, when the fingers are curled in the direction in which the field vectors circulate.) c) The ratio of the angular momentum of a particle to $\hbar$ is its spin quantum number. Determine the spin quantum number of the photon.

What is the Poynting vector at a distance of $12.0 \mathrm{~km}$ from a radio tower that transmits $3.00-10^4 \mathrm{~W}$ of power? Assume that the radio waves that hit the Earth are reflected back into space. a) Are the radio waves coming from this transmitter polarized or not? b) What is the root-mean-square value of the electric force on an electron at this location?