(a) Explanation Given info: Side length of three dimensional box is 8.00 × 10 − 11 m . Write the expression for the energy of the particle in Three dimensional box. E n X , n Y , n Z = ( n X 2 + n Y 2 + n Z 2 ) π 2 ℏ 2 2 m L 2 (1) Here, E n X , n Y , n Z is the energy of the energy of the particle in three dimensional box ( n X , n Y , n Z ) are the quantum numbers of the state n X , n Y and n Z can take only positive integer values m is the mass of the electron L is the length of the box h is the Planck’s constant ℏ is h 2 π Substitute 1 for n X , 1 for n Y , 1 for n Z in the above equation to get E 1 , 1 , 1 . E 1 , 1 , 1 = 3 π 2 ℏ 2 2 m L 2 (2) Substitute 2 for n X , 2 for n Y , 1 for n Z in the above equation to get E 2 , 2 , 1 . E 2 , 2 , 1 = 9 π 2 ℏ 2 2 m L 2 (3) Subtract the equation (1) from (2) to get separation between the E 1 , 1 , 1 and E 2 , 1 , 1 . E 2 , 2 , 1 − E 1 , 1 , 1 = 9 π 2 ℏ 2 2 m L 2 − 3 π 2 ℏ 2 2 m L 2 = 3 π 2 ℏ 2 m L 2 Substitute 1.055 × 10 − 34 J .s for ℏ , 9.109 × 10 − 31 kg for m and 8.00 × 10 − 11 m for L in the above equation to find E 2 , 2 , 1 − E 1 , 1 , 1

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

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Author: Hugh D. Young, Roger A. Freedman

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Chapter 41, Problem 41.3E

(a)

To determine

Wavelength of the photon emitted when an electron in a three dimensional box of side length 8.00×10−11 m makes a transition from the nX=2 , nY=2 , nZ=1 state to the nX=1 , nY=1 , nZ=1 state.

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Chapter 41, Problem 41.2E

Chapter 41, Problem 41.4E

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Chapter 41 Solutions

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

Ch. 41.1 - Prob. 41.1TYU Ch. 41.2 - Prob. 41.2TYU Ch. 41.3 - Prob. 41.3TYU Ch. 41.4 - In this section we assumed that the magnetic field...Ch. 41.5 - In which of the following situations is the...Ch. 41.6 - Prob. 41.6TYU Ch. 41.7 - Prob. 41.7TYU Ch. 41.8 - Prob. 41.8TYU Ch. 41 - Prob. 41.1DQ Ch. 41 - Prob. 41.2DQ

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Wavelength of the photon emitted when an electron in a three dimensional box of side length 8.00 × 10 − 11 m makes a transition from the n X = 2 , n Y = 2 , n Z = 1 state to the n X = 1 , n Y = 1 , n Z = 1 state.

Solution Summary: The author explains the wavelength of the photon emitted when an electron in a three dimensional box of side length 8.00times 10-11

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Wavelength of the photon emitted when an electron in a three dimensional box of side length 8.00×10−11 m makes a transition from the nX=2 , nY=2 , nZ=1 state to the nX=1 , nY=1 , nZ=1 state.

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