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

One App. One Place for Learning.

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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

Measurements

Electric Charge Field and Potential

Dynamics

Fundamentals of Physics

Magnetism and Electromagnetic Induction

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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 ?