Chapter 39: Q22P (page 1216)

An electron is contained in the rectangular corral of Fig. 39-13, with widths $L_{x} = 800 pm$ and $L_{y} = 1600 pm$ . What is the electron’s ground-state energy?

Short Answer

Expert verified

The ground state energy of the electron is 0.7375 eV.

Step by step solution

Introduction:

The electron is a subatomic particle whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family and are generally thought to be elementary particles because they have no known components or substructure.

Solution:

The energy of the electron in a rectangular corral is.

$E_{n} = \frac{h^{2}}{8 m} (\frac{n_{x}^{2}}{L_{x}^{2}} + \frac{n_{y}^{2}}{L_{y}^{2}})$

Here, the Planck constant is $h = 6.63 \times 10^{- 34} J . s$ and the mass of the electron is $m = 9.1 \times 10^{- 31} kg$ .

Here the widths is,

$L_{x} = 800 pm = 800 \times 10^{- 12} m L_{x} = 1600 pm = 1600 \times 10^{- 12} m$

For ground state $n_{x} = 1, n_{y} = 1$ .

$E_{n} = \frac{{(6.63 \times 10^{- 34} Js)}^{2}}{8 (9.1 \times 10^{- 31} kg)} (\frac{{(1)}^{2}}{(800 \times 10^{- 12} m^{2})}) = 0.6038 (\frac{1}{64} + \frac{1}{256}) \times 10^{- 17} J = 0.0118 \times 10^{- 19} J = 1.18 \times 10^{- 19} J E_{n} = \frac{(1.18 \times 10^{- 19} J)}{(1.6 \times 10^{- 19} J / eV)} = 0.7375 eV$

Hence, the electrons ground state energy is 0.7375 eV.

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An electron is contained in the rectangular corral of Fig. 39-13, with widths $L_{x} = 800 pm$ and $L_{y} = 1600 pm$ . What is the electron’s ground-state energy?

Short Answer

Step by step solution

Introduction:

Solution:

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An electron is contained in the rectangular corral of Fig. 39-13, with widths Lx=800pm andLy=1600pm. What is the electron’s ground-state energy?

Short Answer

Step by step solution

Introduction:

Solution:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Physical Quantities And Units

Further Mechanics and Thermal Physics

Classical Mechanics

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Translational Dynamics

Study anywhere. Anytime. Across all devices.

An electron is contained in the rectangular corral of Fig. 39-13, with widths $L_{x} = 800 pm$ and $L_{y} = 1600 pm$ . What is the electron’s ground-state energy?