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 Laboratory Techniques 
 An Introduction to MATHCAD

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 Review of Last Week
 Arrays, Vectors and Matrices
 Simple matrix & vector maths
 Statistics
 Plotting & analysing data with vectors

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 Entering data with the Input Table
 Extracting columns from a matrix
 Creating simple XY graphs
 Formatting graphs
 Slope & Intercept

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 Check on values of vectors

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 Add to graph to show uncertainty in y values.
 Create vector of ‘High’ values
 Create vector of ‘Low’ values
 Add as traces to yaxis
 Add extra xaxis variables
 Format as error bars

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 Use vector maths to get ‘high’ and ‘low’ vectors

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 Use vector maths to preprocess data before graphing
 Use knowledge of physics to get data into a straight line format

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 Photoelectrons emitted from metal surface under illumination
 Illuminate metal with light of different wavelength
 Measure energy of emitted electrons (Stopping Potential)
 Keller, Gettys & Skove p976

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 Equation given in terms of frequency
 Experimental data given in wavelength è convert

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  n=frequency (Hz)
  c= velocity of light (»3x10^{8}m/s)
  l= wavelength (m)
  Valid for all electromagnetic radiation

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 Use resource centre for physical constants
 Watch for confusion of e & q
 Useful functions (lookup in help system)
 slope(vx,vy) è
slope of line
 intercept(vx,vy) è
intercept with axis

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 Vs è Stopping Potential
 n è Frequency of radiation
 n0 è Threshold frequency
 h è Planck’s constant
 q è Electron Charge

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 Systems in the form:
Y=Ae^{Bx}
 Examples:
 Cooling
 Radioactive Decay
 Compound Interest
 B is time constant or rate constant

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 Take logs of Y values
è straight
line
 intercept gives ln(A)
 slope gives B

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 Data in input table as before
 Extract Columns

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 Straight line => power law
 Need to get slope & intercept

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 Take log of y data
 Calculate slope & intercept
 Display A&B
 Create model

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 Use of Input Table
 Column Extract Operator M^{<>}
 Add units if needed
 Plot vector vs vector
 Add Error bars

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 Extract Information from data
 Preprocessing
 Handling power law data
 Create model & compare with data
