Explanation Given data: Length of the box is 0.7 nm. Initial energy level of the electron is 2. Final energy level of the electron is 0. Formula used: Write the expression for the energy of the nth quantum state. E n = n 2 E 1 (1) Here, E n is the energy of the nth quantum state and E 1 is the energy of the lowest energy level. Write the expression for minimum energy of confined electron. E n = h 2 8 m L 2 n 2 (2) Here, E is the energy, h is the plank’s constant with value 6.63 × 10 − 34 J ⋅ s , m is the mass of the electron, n is the integral multiple, and L is the length of the box. Write the expression for photon’s energy and wavelength. E photon = h c λ (3) Here, h is the plank’s constant with value 6.63 × 10 − 34 J ⋅ s , c is the speed of light with value 3.0 × 10 8 m s , and λ is the wavelength. Explanation: Substitute 6.63 × 10 − 34 J ⋅ s for h , 0.7 × 10 − 9 m for L and 9.11 × 10 − 31 kg for m in equation (2), E n = ( 6.63 × 10 − 34 J ⋅ s ) 2 8 × ( 9.11 × 10 − 31 kg ) ( 0.7 × 10 − 9 m ) 2 × ( n ) 2 = ( 6.63 × 10 − 34 J ⋅ s ) 2 35.7112 × 10 − 49 kg ⋅ m 2 × ( n ) 2 = ( 1.231 × 10 − 19 J ) × ( n ) 2 For initial energy level of electron ( n = 1 ) , substitute 1 for n , E 1 = ( 1

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Chapter 28, Problem 69GP

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The wavelength of the emitted photon.

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Chapter 28 Solutions

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