Rutheford successfully used classical mechanics to account for the scattering pattern of alphaparticles by heavy nuclei: he treated the alpha particle as a point mass that follows a hyperbolic trajectory under the repulsion of a ﬁxed point nucleus. But the de Broglie view of the wave nature of particles raises some awkward questions about the validity of Rutherford's analysis.

(a) Calculate the de Broglie wavelength of a 6-McV alpha particle.

(b) Compare your result for (a) with the classical distance of closest approach in a head-on collision of a 6-MeV alpha particle with a gold nucleus (Z = 79). Neglect the recoil of the nucleus.

(c) Do you expert that classical mechanics will be valid describe this encounter? ls your conclusion strengthened or reversed if one takes account of the fact that the alpha particle loses momentum as it approaches the nucleus?

(a) We wish to calculate the de Broglie wavelength of a 6-MeV alpha particle.

We have

(b) We wish to calculate the classical distance ...

Solution Summary

We use the classical model of Rutherford scattering to compute the distance of closest approach of a 6 MeV alpha particle to a gold nucleus, then we compare this distance to the de Broglie wavelength of a 6 MeV alpha particle to see if the classical model is a good approximation.

A beam of particles strikes a wall containing 2 x 10^29 atoms per m^3. Each atom behaves like a sphere of radius 3 x 10^-15m. Find the thickness of wall that exactly half the particles will penetrate without scattering. What Thickness would be needed to stop all but one particle in 10^6 ?
Answer should be: 0.123m and 2.44m

Listed below are measures of pain intensity before and after using the proprietary drug Duragesic.
The data are listed in order by row, and corresponding measures are from the same subject before and after the treatment. For example, the first subject had a measure of 1.2 before the treatment and a measure of 0.4 after the t

210Po is used as a source of 5.2 [MeV] alpha particles in a Rutherford experiment. The alpha particles are directed at a gold foil of thickness 2µm (2 x 10^6 meters) at a rate of 100000 particles per minute. The scattered particles are detected on a screen of area 1cm^2 at a distance of 12cm. Use the Rutherford formula to predi

6. Use the following data to draw a scatter-plot and estimate a correlation coefficient.
Subject X Y
1 1 8
2 2 7
3 5 5
4 2 4
5 6 5
6 1 3
7 5 4
8 5 8
9 6 7

Below are four bivariate data sets and the scatter plot for each. (Note that each scatter plot is displayed on the same scale.) Each data set is made up of sample values drawn from a population. Please see the attachment.

Rutherford observed that an alpha particle (Q1 = 2 x 1.6 x 10^-19 coulomb) having a kinetic energy of 7.68 x 10 ^6 electron volts (7.68 x 10^6 x 1.6 x 10^-19 joule) rebounds backward in a head on collision with a gold nucleus (Q2 = 79 x 1.6 x 10^-19 coulomb).
a. What is the distance of closest approach where the electrostatic p

3) Display the data in scatter plot. Calculate the linear correlation coefficient. Use the scatterplot to make a conclusion about
the type of correlation. x: 0 1 2 3 4
y: 0.5 3 2 4 3.5
find the correlation coefficient.
Choose the statement suggested by the scatter plot and the correlation coef

Given the following data, create a scatter diagram (using Excel), click on the points as demonstrated in the Excel workbook, and have Excel place the regression equation and coefficient of correlation on the graph for you. Interpret the results (in English).
Years of Education Annual Income (000's)
6