Q22P An electron is contained in the ... [FREE SOLUTION]

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鈥檚 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 $h = 6.63 脳 10^{- 34} J . s$ and the mass of the electron is $m = 9.1 脳 10^{- 31} kg$ .

Here the widths is,

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

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

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

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鈥檚 ground-state energy?

Short Answer

Step by step solution

Introduction:

Solution:

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91影视

An electron is contained in the rectangular corral of Fig. 39-13, with widths Lx=800pm andLy=1600pm. What is the electron鈥檚 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

Oscillations

Classical Mechanics

Famous Physicists

Astrophysics

Solid State Physics

Physical Quantities And Units

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鈥檚 ground-state energy?