You want to study a biological spocimen by mcans of a...

You want to study a biological spocimen by mcans of a wavelength of $10.0 \mathrm{nm},$ and you have a choice of using electromagnetic waves or an electron microscope. (a) Calculate the ratio of the energy of a 10.0 -nm-wavelength photon to the kinetic energy of a 10.0 -nm-wavelength electron. (b) In view of your answer to part (a), which would be less damaging to the specimen you are studying; photons or electrons?

Key Concepts

Energy Comparison and Specimen Damage Consideration

Comparing the energy of a photon to the kinetic energy of an electron having the same wavelength is crucial when assessing the potential damage to a biological specimen. Higher energy particles can cause more extensive structural damage. Therefore, by analyzing the energy ratio, one can determine which type of probe—photons or electrons—is less likely to impart damaging energy to delicate biological samples. This concept is integral in microscopy methods and materials research to optimize imaging while minimizing sample degradation.

Photon Energy Calculation

This concept involves calculating the energy of a photon using the fundamental equation E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the photon. This relationship is essential in understanding the energy content of electromagnetic radiation at different wavelengths and is a key component in fields such as quantum mechanics and spectroscopy.

De Broglie Wavelength and Electron Kinetic Energy

The de Broglie wavelength concept posits that particles, like electrons, exhibit wave-like properties with a wavelength ? = h/p, where p is momentum. This relationship is used to determine the momentum—and subsequently the kinetic energy—of electrons when a specific wavelength is desired. The kinetic energy of an electron, given by K = p²/(2m), where m is the electron mass, allows for a direct comparison between the energies of photons and electrons having the same wavelength.

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