Chapter 6: Q21E (page 1355)

An electron is bound in a square well of depth $U_{0} = 6 E_{1 - 1 DW}$ . What is the width of the well if its ground state energy is $2.00 eV$ ?

Short Answer

Expert verified

The width of the well is $3.43 \times 10^{- 10} m$ , if its ground state energy is $2.00 eV$ .

Step by step solution

Define the energy level.

The energy levels of a particle of mass $m$ in a box width $L$ is:

$E_{n} = \frac{P^{2}}{2 m} = \frac{n^{2} h^{2}}{8 m L^{2}} = \frac{n^{2} π^{2} h^{2}}{2 m L^{2}} (n = 1, 2, 3 . . .)$

The ground state energy as a fraction of the ground-level energy for an infinitely deep well $(E_{1 - IDW})$ is given by:

$E_{1} = 0.625 E_{1 - 1 D W}$

Determine the width of the well.

Given that, the energy level of square well of depth is $U_{0} = 6 E_{1 - I D W}$ and ground state energy is $2.00 eV$ .

The ground-state energy $E_{1}$ :

$E_{1} = 2.00 \times (\frac{1.60 \times 10^{- 19}}{1}) = 3.60 \times 10^{- 19}$

The mass of electron is $9.11 \times 10^{- 31}$ and value of $h = 1.055 \times 10^{- 34} J \cdot s$ .

The width of the well is:

$L = \sqrt{\frac{0.625 π^{2} h^{2}}{2 m E_{1}}}$

$= π (1.055 \times 10^{- 34}) \sqrt{\frac{0.625}{2 (9.11 \times 10^{- 31}) (3.20 \times 10^{- 19})}} = 3.43 \times 10^{- 10} m$

Hence, the width of the well is

3.43 \times 10^{- 10} m

, if its ground state energy is

2.00 eV

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An electron is bound in a square well of depth $U_{0} = 6 E_{1 - 1 DW}$ . What is the width of the well if its ground state energy is $2.00 eV$ ?

Short Answer

Step by step solution

Define the energy level.

Determine the width of the well.

One App. One Place for Learning.

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An electron is bound in a square well of depthU0=6E1-1DW. What is the width of the well if its ground­ state energy is2.00eV?

Short Answer

Step by step solution

Define the energy level.

Determine the width of the well.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Circular Motion and Gravitation

Oscillations

Fluids

Physics of Motion

Measurements

Study anywhere. Anytime. Across all devices.

An electron is bound in a square well of depth $U_{0} = 6 E_{1 - 1 DW}$ . What is the width of the well if its ground state energy is $2.00 eV$ ?