Explanation Given information: The lowest transition of electron produces a photon of wavelength 450 nm. Formula used: The expression for the difference in energy levels is given by Δ E = E 2 − E 1 ( 1 ) Where, E 2 and E 1 are energy of the highest and lowest energy levels, respectively. The expression for the energy of the n t h level is given by E n = n 2 ℏ 2 π 2 2 m L 2 ( 2 ) Where, n is the number of energy level. ℏ is reduced Planck’s constant, ℏ = h 2 π . h is Planck’s constant, h = 6.64 × 10 − 34 J ⋅ s m is mass of electron = 9.1 × 10 − 31 kg , and L is width of the quantum well. Substitute for ℏ in equation: E n = n 2 h 2 8 m L 2 ( 3 ) The difference in the energy of the corresponding energy level is given by Δ E = h c λ ( 4 ) Where, λ is wavelength. h is Planck’s constant. c is speed of light = 3 × 10 8 m/s Lowest energy transition will occur from first excited state to the ground state, that is n = 2 → n = 1 Substitute the numerical values in equation ( 3 ) : E n = n 2 ( 6.64 × 10 − 34 ) 2 8 × 9.1 × 10 − 31 × L 2 = n 2 × 44

2nd Edition

ISBN: 9780805303087

Author: Randy Harris

Publisher: Addison Wesley

See similar textbooks

Question

Chapter 5, Problem 25E

To determine

The width of quantum well in which an electron is trapped.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5, Problem 24E

Chapter 5, Problem 26E

Students have asked these similar questions

an electron bound inside a quantum harmonic oscillator potential. what is the wavelength of the photon absorbed if the electron makes a transition from the ground state, with energy 0.89 [eV], to the fourth excited state?

At what temperature would we find about half as many hydrogen atoms in first excited state as in the groundstate?..

Given a quantum particle trapped in aninfinite 1 D potential well of length, L the ratio of energy eigen values of 7 th excited state to 5 th excited state is

Chapter 5 Solutions

Modern Physics

Ch. 5 - Prob. 1CQ Ch. 5 - Prob. 2CQ Ch. 5 - Prob. 3CQ Ch. 5 - Prob. 4CQ Ch. 5 - Prob. 5CQ Ch. 5 - Prob. 6CQ Ch. 5 - Prob. 7CQ Ch. 5 - Prob. 8CQ Ch. 5 - Prob. 9CQ Ch. 5 - Prob. 10CQ

Ch. 5 - Prob. 11CQ Ch. 5 - Prob. 12CQ Ch. 5 - Prob. 13CQ Ch. 5 - Prob. 14CQ Ch. 5 - Prob. 15CQ Ch. 5 - Prob. 16CQ Ch. 5 - Prob. 17CQ Ch. 5 - Prob. 18CQ Ch. 5 - Prob. 19E Ch. 5 - Prob. 20E Ch. 5 - Prob. 21E Ch. 5 - Prob. 22E Ch. 5 - Prob. 23E Ch. 5 - Prob. 24E Ch. 5 - Prob. 25E Ch. 5 - Prob. 26E Ch. 5 - Prob. 27E Ch. 5 - Prob. 28E Ch. 5 - Prob. 29E Ch. 5 - Prob. 30E Ch. 5 - Prob. 31E Ch. 5 - Prob. 32E Ch. 5 - Prob. 33E Ch. 5 - Prob. 34E Ch. 5 - Prob. 35E Ch. 5 - Prob. 36E Ch. 5 - Prob. 37E Ch. 5 - Prob. 38E Ch. 5 - Prob. 39E Ch. 5 - Prob. 40E Ch. 5 - Prob. 41E Ch. 5 - Prob. 42E Ch. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44E Ch. 5 - Prob. 45E Ch. 5 - Prob. 46E Ch. 5 - Prob. 47E Ch. 5 - Prob. 48E Ch. 5 - Prob. 49E Ch. 5 - Prob. 50E Ch. 5 - Prob. 51E Ch. 5 - Prob. 52E Ch. 5 - Prob. 53E Ch. 5 - Prob. 54E Ch. 5 - Prob. 55E Ch. 5 - Prob. 56E Ch. 5 - Prob. 57E Ch. 5 - Prob. 58E Ch. 5 - Prob. 59E Ch. 5 - Prob. 60E Ch. 5 - Prob. 61E Ch. 5 - Prob. 62E Ch. 5 - Prob. 63E Ch. 5 - Prob. 64E Ch. 5 - Prob. 65E Ch. 5 - Prob. 66E Ch. 5 - Prob. 67E Ch. 5 - Prob. 68E Ch. 5 - Prob. 69E Ch. 5 - Prob. 70E Ch. 5 - Prob. 71E Ch. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CE Ch. 5 - Prob. 74CE Ch. 5 - Prob. 75CE Ch. 5 - Prob. 76CE Ch. 5 - Prob. 77CE Ch. 5 - Prob. 78CE Ch. 5 - Prob. 79CE Ch. 5 - Prob. 80CE Ch. 5 - Prob. 81CE Ch. 5 - Prob. 82CE Ch. 5 - Prob. 83CE Ch. 5 - Prob. 84CE Ch. 5 - Prob. 85CE Ch. 5 - Prob. 86CE Ch. 5 - Prob. 87CE Ch. 5 - Prob. 88CE Ch. 5 - Consider the differential equation...Ch. 5 - Prob. 90CE Ch. 5 - Prob. 91CE Ch. 5 - Prob. 92CE Ch. 5 - Prob. 93CE Ch. 5 - Prob. 94CE Ch. 5 - Prob. 95CE Ch. 5 - Prob. 96CE Ch. 5 - Prob. 97CE Ch. 5 - Prob. 98CE

Knowledge Booster

The width of quantum well in which an electron is trapped.

Solution Summary: The author explains that the lowest energy transition of electron produces a photon of wavelength 450 nm.

The width of quantum well in which an electron is trapped.

Want to see the full answer?

Chapter 5 Solutions