a) The energy difference between the electrons ground state and its first excited state b) The quantum number n would the energy difference between adjacent energy levels be 1.0 e V which is measurable, unlike the result of (a) c) The multiple of the electron’s rest energy would give the electrons total energy. d) Would the electron be relativistic?

Question

An electron is confined to a narrow evacuated tube of length 3.0 m; the tube functions as a one-dimensional infinite potential well. (a) What is the energy difference between the electron’s ground state and its first excited state? (b) At what quantum number n would the energy difference between adjacent energy levels be 1.0 eV—which is measurable, unlike the result of (a)? At that quantum number, (c) what multiple of the electron’s rest energy would give the electron’s total energy and (d) would the electron be relativistic?

Answer 1

Question

Chapter 39, Problem 60P

To determine

To find:

a) The energy difference between the electrons ground state and its first excited state

b) The quantum number n would the energy difference between adjacent energy levels be 1.0 eV which is measurable, unlike the result of (a)

c) The multiple of the electron’s rest energy would give the electrons total energy.

d) Would the electron be relativistic?

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Students have asked these similar questions

An electron is confined to a narrow evacuated tube of length 3.0 m; the tube functions as a one-dimensional infinite potential well. (a) What is the energy difference between the electron’s ground state and its first excited state? (b) At what quantum number n would the energy difference between adjacent energy levels be 1.0 eV—which is measurable, unlike the result of (a)? At that quantum number, (c) what multiple of the electron’s rest energy would give the electron’s total energy and (d) would the electron be relativistic?

An electron is trapped in a one-dimensional region of length 1.00 x 10-10 m (a typical atomic diameter). (a) Find the energies of the ground state and first two excited states. (b) How much energy must be supplied to excite the electron from the ground state to the sec- ond excited state? (c) From the second excited state, the electron drops down to the first excited state. How much energy is released in this process?

Question 1An electron is trapped in a region between two infinitely high energy barriers. In the regionbetween the walls the potential energy of the electron is zero. The normalised wavefunction of the electron in the region between the walls is ?(?) = ? sin ??, where ? =0.50 nm−1/2and ? = 1.18 nm−1.(a) Calculate the energy of the electron in this state of motion.Question 2In some physical situations, the behaviour of an electron can be approximated as if theelectron were bound to an equilibrium position by a spring force (?(?) = −??, ?(?) =??22,where ? is the spring constant). Suppose such an electron were in the first excited state,with a wave function ?(?) = ???−??2, where ? is a constant, ? = √??/2ℏ and ?represents the distance of the electron from its equilibrium position.(a) Calculate the energy of the electron in terms of ? and its mass ?.(b) If the electron behaved like a classical oscillating particle, the largest value of ?would be ??. Show that ?? = √3ℏ. (??)−1/4.