Explanation When an electron makes transition from M shell to K shell, a photon is emitted. Write the expression for the energy of electrons in K shell. E K = − Z 2 ( 13.6 eV ) (I) Here, E K is the energy of electrons in K shell, and Z is the atomic number. When the electron is in the M shell, the nuclear charge of the atom is shielded by the nine electrons. Write the expression for the energy in M shell. E M = − ( Z − 9 ) 2 13.6 eV n 2 (II) Here, E M is the energy of electron in the M shell, and n is the principle quantum number. Energy of the photon released when the electron falls from M shell to K shell is equal to the difference in the energies of M shell and K shell. Write the expression for the energy of the photon released. E photon = E M − E K (III) Here, E photon is the energy of the photon released. Use expressions (I) and (II) in expression (III). E photon = − ( Z − 9 ) 2 13.6 eV n 2 − ( − ( Z ) 2 ( 13.6 eV ) ) = ( 13.6 eV ) [ − ( Z − 9 ) 2 n 2 + Z 2 ] (IV) Expand the terms in expression (IV). E photon = ( 13.6 eV ) [ − ( Z 2 − 18 Z + 81 n 2 ) + Z 2 ] (V) Write the expression for the energy of the photon. E photon = h c λ (VI) Here, h is the Planck’s constant, c is the speed of light, and λ is the wavelength of photon

Physics for Scientists and Engineers with Modern Physics, Technology Update

9th Edition

ISBN: 9781305401969

Author: SERWAY, Raymond A.; Jewett, John W.

Publisher: Cengage Learning

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Chapter 42, Problem 57P

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Identify the element which emits x-ray of wavelength 0.101 nm.

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Chapter 42, Problem 56P

Chapter 42, Problem 58P

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When an electron drops from the M shell (n = 3) to a vacancy in the K shell (n = 1), the measured wavelength of the emitted x - ray is found to be 0.101 nm. Identify the element.

4. a. An electron in a hydrogen atom falls from an initial energy level of n-5 to a final level of n - 2. Find the energy, frequency, and wavelength of the photon that will be [For hydrogen: E-13.6 eV/n²] emitted for this sequence. b. A photon of energy 2.794 eV is absorbed by a hydrogen atom, causing its electron to be released with a kinetic energy of 2.250 eV. In what energy level was the electron? c. Find the wavelength of the matter wave associated with a proton moving at a speed of 350 m/s.

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Chapter 42 Solutions

Physics for Scientists and Engineers with Modern Physics, Technology Update

Ch. 42.3 - Prob. 42.1QQ Ch. 42.3 - Prob. 42.2QQ Ch. 42.4 - Prob. 42.3QQ Ch. 42.4 - Prob. 42.4QQ Ch. 42.8 - Prob. 42.5QQ Ch. 42 - Prob. 1OQ Ch. 42 - Prob. 2OQ Ch. 42 - Prob. 3OQ Ch. 42 - Prob. 4OQ Ch. 42 - Prob. 5OQ

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Identify the element which emits x-ray of wavelength 0.101 nm .

Solution Summary: The author identifies the element which emits x-ray of wavelength 0.101nm. When an electron makes transition from M shell to K shell, a photon is emitted.

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Identify the element which emits x-ray of wavelength 0.101 nm.

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Chapter 42 Solutions