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Chapter 38: Q 67P (page 1184)

Question:The uncertainty in the position of an electron along an xaxis

is given as 50pm, which is about equal to the radius of a hydrogen

atom. What is the least uncertainty in any simultaneous measurement

of the momentum component of this electron?

Short Answer

Expert verified

The least uncertainty in the momentum component pxof this electron is

∆px=2.1×10-24kgms

Step by step solution

01

Identifying the data given in the question.

The uncertainty in the position of the electron is

∆x=50pm=50×10-12m

02

Concept used to solve the question

Heisenberg’s Uncertainty Principle

According to Heisenberg’s Uncertainty Principle, the uncertainty in position and momentum are related as,

∆x∆px≥h2π

Where;

∆x is uncertainty in position along the axis.

∆pxis uncertainty in momentum along the axis.


his plank’s constant.

03

Finding the least uncertainty in the momentum component px

According to Heisenberg’s Uncertainty Principle

∆x∆px≥h2π

The least uncertainty possible when

∆x∆px=h2π

Therefore,

∆px=h2π∆x

Substituting the values,

∆px=6.634×10-34J.s2π50×10-12m=2.1×10-24kgms-1

Hence the least uncertainty in the momentum component pxof this electron is

∆px=2.1×10-24kgms-1

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Most popular questions from this chapter

Monochromatic light (that is, light of a single wavelength) is to be absorbed by a sheet of photographic film and thus recorded on the film. Photon absorption will occur if the photon energy equals or exceeds 0.6eV, the smallest amount of energy needed to dissociate an AgBr molecule in the film. (a) What is the greatest wavelength of light that can be recorded by the film? (b) In what region of the electromagnetic spectrum is this wavelength located?

What (a) frequency, (b) photon energy, and (c) photon momentum magnitude (in keV/c) are associated with x-rays having wavelength 35.0pm?

The existence of the atomic nucleus was discovered in 1911by Ernest Rutherford, who properly interpreted some experiments in which a beam of alpha particles was scattered from a metal foil of atoms such as gold. (a) If the alpha particles had a kinetic energy of 7.5MeV, what wads their de Broglie wavelength? (b) Explain whether the wave nature of the incident alpha particles should have been taken into account in interpreting these experiments. The mass of an alpha particle is4.00u (atomic mass units), and its distance of closest approach to the nuclear center in these experiments was about 30fm. (The wave nature of matter was not postulated until more than a decade after these crucial experiments were performed.)

Let K be the kinetic energy that a stationary free electron gains when a photon scatters from it. We can plot K versus the angle ϕat which the photon scatters; see curve 1 in Fig. 38-21. If we switch the target to be a stationary free proton, does the end point of the graph shift (a) upward as suggested by curve 2, (b) downward as suggested by curve 3, or (c) remain the same?

In a Compton-shift experiment, light (in the x-ray range) is scattered in the forward direction, atϕ=0 in Fig. 38-3. What fraction of the light’s energy does the electron acquire?
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