Chapter 39: Q5P (page 1215)

What must be the width of a one-dimensional infinite potential well if an electron trapped in it in the $n = 3$ state is to have an energy of 4.7 eV ?

Short Answer

Expert verified

0.85 nm

Step by step solution

Given data

$E_{n} = 4.7 e V n = 3$

Energy in a potential well

The $n^{t h}$ state energy of a particle of mass $m$ in an infinite potential well of width L is

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

Determining the width of the potential well

Here h is the Planck's constant having value

$h = 6.626 \times 10^{- 34} J . s and c = 2.998 \times 10^{8} m / s, h_{c} = \frac{(6.626 \times 10^{- 34} J . s) (2.998 \times 10^{8} m / s)}{(1.602 \times 10^{- 19} J / eV) (10^{- 9} m / nm)} = 1240 eV . nm$

Using the $m c^{2}$ value for an electron from Table 37-3 $(511 \times 10^{3} eV)$ , Eq.39 – 4 can be rewritten as

$E_{n} = \frac{n^{2} h^{2}}{8 m L^{2}} = \frac{n^{2} {(h_{c})}^{2}}{8 (m c^{2}) L^{2}}$

For $n = 3$ ,

$L = \frac{n (h_{c})}{\sqrt{8 (m c^{2}) (E_{n})}} = \frac{3 (1240 eV . nm)}{\sqrt{8 (511 \times 10^{3} eV) (4.7 eV)}} = 0.85 nm$

Thus, the width is $0.85 nm$ .

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What must be the width of a one-dimensional infinite potential well if an electron trapped in it in the $n = 3$ state is to have an energy of 4.7 eV ?

Short Answer

Step by step solution

Given data

Energy in a potential well

Determining the width of the potential well

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What must be the width of a one-dimensional infinite potential well if an electron trapped in it in the n=3 state is to have an energy of 4.7 eV ?

Short Answer

Step by step solution

Given data

Energy in a potential well

Determining the width of the potential well

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

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Study anywhere. Anytime. Across all devices.

What must be the width of a one-dimensional infinite potential well if an electron trapped in it in the $n = 3$ state is to have an energy of 4.7 eV ?