32. Electromagnetic Waves

A laser beam shines straight up onto a flat, black foil of mass m. Find an expression for the laser power P needed to levitate the foil.

INT Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of 500 nm?

What is the de Broglie wavelength of a 200 g baseball with a speed of 30 m/s?

The diameter of the nucleus is about 10 fm. What is the kinetic energy, in MeV, of a proton with a de Broglie wavelength of 10 fm?

What is the quantum number of an electron confined in a 3.0-nm-long one-dimensional box if the electron’s de Broglie wavelength is 1.0 nm?

The diameter of the nucleus is about 10 fm. A simple model of the nucleus is that protons and neutrons are confined within a one-dimensional box of length 10 fm. What are the first three energy levels, in MeV, for a proton in such a box?

(II) (a) Suppose for a conventional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? (b) Suppose, instead, that the X-rays come from a point source (as in Fig. 35–31) that is 15 cm in front of a human body which is 25 cm thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that result.

<IMAGE>

(II) How much energy is transported across a 1.00-cm² area per hour by an EM wave whose E field has an rms strength of 25.8 mV/m?

(II) What is the relative brightness of the Sun as seen from Jupiter, as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the Earth is.)

Estimate how long an AM antenna would have to be if it were (a) ½ ⋋ or (b) ¼ ⋋ AM radio is roughly 1 MHz (530 kHz to 1.7 MHz).

(I) Electromagnetic waves and sound waves can have the same frequency. (a) What is the wavelength of a 1.00-kHz electromagnetic wave? (b) What is the wavelength of a 1.00-kHz sound wave? (The speed of sound in air is 341 m/s.) (c) Can you hear a 1.00-kHz electromagnetic wave?

(II) How long would it take a message sent as radio waves from Earth to reach Mars when Mars is (a) nearest Earth, (b) farthest from Earth? Assume that Mars and Earth are in the same plane and that their orbits around the Sun are circles (Mars is 230 x 10⁶ km from the Sun).

(II) Pulsed lasers used for science and medicine produce very brief bursts of electromagnetic energy. If the laser light wavelength is 1062 mm (Neodymium–YAG laser), and the pulse lasts for 32 picoseconds, how many wavelengths are found within the laser pulse? How brief would the pulse need to be to fit only one wavelength?

(I) The $\overrightarrow{E}$ field in an EM wave has a peak of 23.5 mV/m. What is the average rate at which this wave carries energy across unit area per unit time?

(II) The magnetic field in a traveling EM wave has an rms strength of 22.5 nT. How long does it take to deliver 415 J of energy to 1.00 cm² of a wall that it hits perpendicularly?