Chapter 39: Q7P (page 1215)

Consider an atomic nucleus to be equivalent to a one dimensional infinite potential well with $L = 1.4 \times 10^{- 14}$ , a typical nuclear diameter. What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)

Short Answer

Expert verified

1.9 GeV

Step by step solution

Given data

The width of the potential well is

$L = 1.4 \times 10^{- 14} m$

Energy in a potential well

The ground state energy of a particle of mass m in an infinite potential well of width L is

$E_{0} = (\frac{h^{2}}{8 m_{e} L^{2}}) n^{2} . . . . . . . . . . . . (1)$

Here h is the Planck's constant having value

$h = 6.63 \times 10^{- 34} J . s$

Determining the ground state energy of electron

The mass of the electron is

$m_{e} = 9.11 \times 10^{- 31} k g$

From equation (I) the ground state energy of electron is

$E_{1} = \frac{{(6.63 \times 10^{- 34} J . s)}^{2}}{8 \times 9.11 \times 10^{- 31} k g \times {(1.4 \times 10^{- 14} m)}^{2}} {(1)}^{2} = 3.07 \times 10^{- 10} \times (1 J) . (1 J \times \frac{1 k g . m^{2} / s^{2}}{1 J}) . (1 s^{2}) . (\frac{1}{1 k g}) . (\frac{1}{1 m^{2}}) = 3.07 \times 10^{- 10} J$

The energy in electron volt is

$E_{1} = 3.07 \times 10^{- 10} \times (1 J \times \frac{0.624 \times 10^{19} e V}{1 J}) = 1.9 \times 10^{9} e V = 1.9 G e V$

The required energy is $1.9 G e V$ .

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Consider an atomic nucleus to be equivalent to a one dimensional infinite potential well with $L = 1.4 \times 10^{- 14}$ , a typical nuclear diameter. What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)

Short Answer

Step by step solution

Given data

Energy in a potential well

Determining the ground state energy of electron

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Consider an atomic nucleus to be equivalent to a one dimensional infinite potential well with L=1.4×10-14, a typical nuclear diameter. What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)

Short Answer

Step by step solution

Given data

Energy in a potential well

Determining the ground state energy of electron

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Space Physics

Geometrical and Physical Optics

Mechanics and Materials

Physics of Motion

Dynamics

Kinematics Physics

Study anywhere. Anytime. Across all devices.

Consider an atomic nucleus to be equivalent to a one dimensional infinite potential well with $L = 1.4 \times 10^{- 14}$ , a typical nuclear diameter. What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)