Explanation 1) Concept: Using equation for the de Broglie wavelength and momentum for unknown particle as well as electron particle and taking the ratio λ p λ e , we can find the value of mass of the particle, and using this value in Appendix B, we can identify the given unknown particle. 2) Formula: i) From Eq.38-17, the de Broglie wavelength is given by λ = h p ii) The momentum is p = m v 3) Given: i) The ratio of de Broglie wavelengths λ p λ e = 1.813 × 10 - 4 ii) The ratio of speeds v p v e = 3 4) Calculations: From Eq.38-17, the wavelength associated with the unknown particle is given by λ p = h p p where, h = 6.626 × 10 - 34 J . s is the Planck constant and p p is momentum of the unknown particle But, we know that p p = m p v p where, m p is mass of the unknown particle and v p is speed of the unknown particle. Substituting in the above equation, we get λ p = h m p v p … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ( 1 ) Similarly, wavelength associated with the electron particle is λ e = h p e Here, p e is momentum of the electron particle. But, we know that p e = m e v e where, m e is mass of the electron particle and v e is speed of the electron particle. Substituting in above equation, we get λ e = h m e v e … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ( 2 ) Therefore, from Eq

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Author: David Halliday, Robert Resnick, Jearl Walker

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Chapter 38, Problem 57P

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The mass of the particle and identify the particle.

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Chapter 38 Solutions

Fundamentals of Physics Extended

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The mass of the particle and identify the particle.

Solution Summary: The author explains how the equation for the de Broglie wavelength and momentum for unknown particle and electron particle can be used to identify the particle.

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To find: The mass of the particle and identify the particle.

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Chapter 38 Solutions

To find:

The mass of the particle and identify the particle.