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Chapter 34: Problem 20

Find the energy in electronvolts of (a) a 1.0 -MHz radio photon, (b) a \(5.0 \times 10^{14}-\mathrm{Hz}\) optical photon, and (c) a \(3.0 \times 10^{18}-\mathrm{Hz}\) X-ray photon.

Short Answer

Expert verified
The energies are approximately \(4.14 \times 10^{-9}\) eV, \(2.07\) eV, and \(12,408\) eV for the radio, optical, and X-ray photon respectively.

Step by step solution

01

Calculate energy in Joules

First calculate the energy in Joules for each photon type using the formula \(E = h \cdot f\). For instance, for a 1.0MHz radio photon the energy would be \(E = (6.626 \times 10^{-34} J\cdot s)(1.0 \times 10^6 s^{-1})=6.626 \times 10^{-28} J \).
02

Convert energy to electronvolts

Second, convert the calculated energy from Joules to electronvolts using the conversion factor \(1 eV = 1.602 \times 10^{-19} J\). For example, for the radio photon the energy would be \( \frac{6.626 \times 10^{-28} J}{1.602 \times 10^{-19} J} \approx 4.14 \times 10^{-9} eV \).
03

Repeat steps 1 and 2 for the other photons

Repeat the above steps for the optical photon with frequency \(5.0 \times 10^{14}\)Hz and for the X-ray photon with frequency \(3.0 \times 10^{18}\)Hz.

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