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Chapter 39: Q6P (page 1215)

A proton is confined to a one-dimensional infinite potential well 100pm wide. What is its ground-state energy?

Short Answer

Expert verified

0.0205eV

Step by step solution

01

Given data

The width of the potential well is

L=100pm=100×1pm×1m1012pm=100×10-12m

02

Energy in a potential well

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

E0=h28meL2n2.........1

Here h is the Planck's constant having value

h=6.63×10-34J.s

03

Determining the ground state energy of proton

The mass of the proton is

mp=1.67×10-27kg

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

E1=6.63×10-34J.s8×1.67×10-27kg×100×10-12m12=3.29×10-21×1J.1J×1kg.m2/s21J.1s2.11kg.1m2=3.29×10-21J

The energy in electron volt is

E1=3.29×10-21J×1J×0.624×1019eV1J=0.0205eV

The required energy is 0.0205 eV .

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Most popular questions from this chapter

What is the probability that an electron in the ground state of the hydrogen atom will be found between two spherical shells whose radii are r and r + ∆r, (a) if r = 0.500a and ∆r=0.010aand (b) if r = 1.00a and ∆r=0.01a, where a is the Bohr radius? (Hint: r is small enough to permit the radial probability density to be taken to be constant between r and r+∆r.)

An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to the energy difference ∆E43 between the levels n = 4 and n = 3 ? (c) Show that no pair of adjacent levels has an energy difference equal to 2∆E43 .

A cubical box of widths Lx=Ly=Lz=Lcontains an electron. What multiple of ,h2/8mL2where, m is the electron mass, is (a) the energy of the electron’s ground state, (b) the energy of its second excited state, and (c) the difference between the energies of its second and third excited states? How many degenerate states have the energy of (d) the first excited state and (e) the fifth excited state?

Calculate the probability that the electron in the hydrogen atom, in its ground state, will be found between spherical shells whose radii are a and 2a , where a is the Bohr radius?

Verify that Eq. 39-44, the radial probability density for the ground state of the hydrogen atom, is normalized. That is, verify that the following is true:∫0∞P(r)dr=1
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