Using the genfit() function, fit the curve to the results of SelectChannels(41,96) and determine the 6 parameters A0..A5 [3 marks]

Leaving the centre channel fixed, write a section of MathCAD to produce a graph showing how the Peak Width Characteristic (A3) varies as the number of channels in the average is varied from 1 to 100. [3 marks]
which may be characterisied by the following parameters:
A0: Background level
A1: Amplitude of Peak #1
A2: Centre of Peak #1
A3: Peak width Characteristic
A4: Amplitude of Peak #2
A5: Centre of Peak #2
Question 8

T he data file http://users.aber.ac.uk/dpl/ph36010/handouts/KEScan.csv contains the results of using the above detector in an electron spectrometer.

The first column in the data file gives the Kinetic Energy of electrons passing through the centre of an analyser containing the detector. The remaining 192 columns in the data give the number of electrons falling on the 192 channels of the detector in one second at each Kinetic Energy.

In this application, the data from a number of adjacent channels will be averaged.

Copy the data file to your own filestore and create a file read component to read the data into an array.

Create a function SelectChannels(width,centre) which returns a vector containing the averaged readings over 'width' detectors centred on detector 'centre'. Thus SelectChannels(41,96) will return a vector showing the average number of counts recieved on channels 75 to 116 for each Kinetic Energy. [3 marks]

Plot SelectChannels(41,96) against the Kinetic energy. Your plot should have 2 gaussian type peaks. [1 mark]

The equation of a curve containing two gaussian peaks is given by the formula:
Question 7
During evaluation of an ion counting detector an experiment was conducted to compare the performance of the new detector with an existing photomultiplier based detector. What is particularly interesting is the maximum count rate delivered by the counting detector and how linear the device is.

In the experiment a beam of ions was switched between the ion counting detector and a photomultiplier. At each point the photomultiplier current was recorded along with the count rate observed on the ion counting detector. The incident beam was varied in intensity over several orders of magnitude.

The data file http://users.aber.ac.uk/dpl/ph36010/handouts/CountRate.csv
holds the results of this experiment. The first column holds the photomultiplier in uA and the second the count rate recorded on the ion detector in counts per second.

Use a file read component to read in the datafile. [1 mark]
Plot the data on a graph with log/log axes. [1 mark]
According to theory, the response of such a detector should follow a curve
given by y=x*A*exp(-B*x), where A is a scale factor and A/B is the time it takes the counting detector to recover between events. Use a curve fitting routine and determine the constants A & B. [4 marks]
Plot the fitted curve on the same log/log plot as the experimental data [1 mark]
By scaling the photomulitplier current by an appropriate factor, you should be able to plot the observed count rate of the detector against the incident count rate, again use log/log axes. [1 mark]
Determine the time in seconds it takes the detector to recover after an event. [2 marks]
Question 6
Copy and paste the example from PH15010 Worksheet 6 about the photoelectric effect. Your example should start with an input table holding the stopping potential data and finish with calculation of the threshold frequency and Planck's constant. [10 marks]
over a range of x-values from 0 to 1, using a suitable increment for x [2 marks]

Calculate the area under the curve, using both symbolic and numeric methods. [3 marks]

Using the above result, together with the area of the unit square, devise a
method for determining a value for p which works by calculating the proportion of points picked at random from within the unit square which lie under the above curve. [5 marks]

Functions that you may find helpful for this problem are:
rnd(), if() and mean()
Question 5
Plot the curve:
Question 4.
A sphere of lead of radius 6 inches is dropped from a height of 4 feet.

Calculate the surface area, volume and mass of the sphere, displaying your results in both metric and imperial units. [3 marks]

Write a function, hsphere(), giving the height of the sphere above the ground as a function of time after the sphere is released. [2 marks]

Write a function, vsphere(), giving the velocity of the sphere as a function of time after the sphere is released. [2 marks]

Draw a graph showing the height of the sphere as a function of time. [2 marks]

Detemine the time that the sphere will hit the ground. [2 marks]

Calculate the velocity (in m/s) that the sphere will hit the ground.(You may neglect air resistance) [2 marks]

Calculate the kinetic energy (in Joules) of the sphere as it hits the ground. [2 marks]
Question 3.
The file http://users.aber.ac.uk/dpl/ph36010/handouts/RValues.txt contains the values of a number of resistors. Copy this file into your own directory.

Create a file read component to read these values into a vector. [2 marks]
Determine the value of the largest, the smallest, the mean and standard deviation along with the total number of resistors. [5 marks]

Create a histogram graph of the values, using an appropriate number of bins to cover the range of values. [5 marks]
Question 2. [4 marks]
Solve the following set of simultaneous equations, using any appropriate technique:
Question 1. [4 marks]
Calculate the surface area, volume and mass of a right circular cone made from quartz. The dimensions of the cone are: base radius 7cm, height 10cm.
This worksheet is a marked assignment to test what you have learned from the course.
This assignment will count towards 50% of the module marks, the remaining 50% will come from the project.

The answers to the exercises should form a single worksheet. Completed worksheets should be emailed to dpl@aber.ac.uk by 23:59 on 17/5/03.

Please ensure that your name appears on the right hand side of the page header and that your email identifier appears on the left hand side of the page footer.

Marks will be given for correctness, layout style, comments, use of units and creative use of material covered in the course. [style=5 marks]

In order to complete the exercises, you may have to do research in the mathCAD resource centre.