< Question 7 of 18 The electron microscope uses the wave property of electrons to observe very small objects. A moving electron has a wavelength described by the de Broglie equation. What would be the wavelength, in m, of an electron with a kinetic energy of 4.50 x 10-1⁹ J, which would be equivalent to the energy of a photon in the visible region? (The mass of an electron is 9.11 × 10-2⁹ g.) 1 4 7 +/- 2 5 8 .

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**Electron Microscopy and de Broglie Wavelengths**

The electron microscope leverages the wave properties of electrons to observe extremely small objects. The wavelength of a moving electron is characterized by the de Broglie equation. This concept can be applied to determine the wavelength of an electron with a known kinetic energy.

**Problem Statement:**

Given an electron with a kinetic energy of \(4.50 \times 10^{-19}\) J, determine its wavelength in meters. This wavelength should be comparable to the energy of a photon within the visible light region.

**Known Values:**
- Kinetic energy of the electron: \(4.50 \times 10^{-19}\) J
- Mass of an electron: \(9.11 \times 10^{-28}\) g

The application of these principles allows for the calculation of wavelengths that are significant in understanding electron behavior in microscopy and quantum mechanics.
Transcribed Image Text:**Electron Microscopy and de Broglie Wavelengths** The electron microscope leverages the wave properties of electrons to observe extremely small objects. The wavelength of a moving electron is characterized by the de Broglie equation. This concept can be applied to determine the wavelength of an electron with a known kinetic energy. **Problem Statement:** Given an electron with a kinetic energy of \(4.50 \times 10^{-19}\) J, determine its wavelength in meters. This wavelength should be comparable to the energy of a photon within the visible light region. **Known Values:** - Kinetic energy of the electron: \(4.50 \times 10^{-19}\) J - Mass of an electron: \(9.11 \times 10^{-28}\) g The application of these principles allows for the calculation of wavelengths that are significant in understanding electron behavior in microscopy and quantum mechanics.
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