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Chapter 39: Q2 (page 1136)

What is the difference between the probability and the probability density?

Short Answer

Expert verified

Probability is a number defining chances of and event to occur whereas probability density is distribution of probability over a region in space.

Step by step solution

01

Concept Used

Difference between probability and probability density is same as difference between charge and charge density.

02

Explanation

Probability: Chances of occurrence of an event is defined as Probability.

More is the likeliness of an even to happen, higher is it's probability.

Probability density is more of a distribution term. If probability of something is distributed over a length or region then probability density comes into play.

For example: Finding and electron in the region x=1 to x=5 will have different probability densities throughout this region.

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Most popular questions from this chapter

Ultrasound pulses with a frequency of 1.000 MHz are transmitted into water, where the speed of sound is 1500 m /s. The spatial length of each pulse is 12 mm.

a. How many complete cycles are contained in one pulse?

b. What range of frequencies must be superimposed to create each pulse?

A 1.0-mm-diameter sphere bounces back and forth between two walls at x=0mmand x=100mm. The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is

a. At exactly x=50.0mm?

b. Between x=49.0mmand x=51.0mm?

c. At x≥75mm?

A proton is confined within an atomic nucleus of diameter 4.0m. Use a one-dimensional model to estimate the smallest range of speeds you might find for a proton in the nucleus.

The probability density for finding a particle at position x is P1x2 = • a 11 - x2 -1 mm … x 6 0 mm b11 - x2 0 mm … x … 1 mm and zero elsewhere. a. You will learn in Chapter 40 that the wave function must be a continuous function. Assuming that to be the case, what can you conclude about the relationship between a and b? b. Determine values for a and b. c. Draw a graph of the probability density over the interval -2 mm … x … 2 mm. d. What is the probability that the particle will be found to the left of the origin?

Consider a single-slit diffraction experiment using electrons. (Single-slit diffraction was described in Section 33.4.) Using Figure 39.5 as a model, draw

a. A dot picture showing the arrival positions of the first 40 or 50 electrons.

b. A graph of |ψ(x)|2for the electrons on the detection screen.

c. A graph of ψ(x)for the electrons. Keep in mind that ψ, as a wave-like function, oscillates between positive and negative.
See all solutions

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