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Schrick - 1492657 -## Set Working Directory to file directory - RStudio approach -setwd(dirname(rstudioapi::getActiveDocumentContext()$path)) - ## Part A: compute binding energy computeBindingEnergy <- function(A, Z){ if (A %% 2 == 1) { @@ -17,14 +14,17 @@ computeBindingEnergy <- function(A, Z){ spin <- -12 } - B <- (15.67*A) - (17.23*(A^(2/3))) - ((0.75)*((Z^2)/(A^(1/3)))) - ((93.2)*(((A-(2*Z))^2)/A)) + (spin/(A^(1/2))) - - return(B) + return((15.67*A)- + (17.23*(A^(2/3)))- + ((0.75)*((Z^2)/(A^(1/3))))- + ((93.2)*(((A-(2*Z))^2)/A))+ + (spin/(A^(1/2)))) } ## Part B: compute Z=28 and A=58 -computeBindingEnergy(58,28) -(15.67*58) - (17.23*(58^(2/3))) - ((0.75)*((28^2)/(58^(1/3)))) - ((93.2)*(((58-(2*28))^2)/58)) + (12/(58^(1/2))) +# Nickel +bind.energy <- computeBindingEnergy(58,28) +cat(round(bind.energy,digits=2),"MeV") ## Part C: table with two columns: nucleons and binding energy per nucleon Z=6 # Carbon @@ -39,9 +39,10 @@ print(carbon_df, row.names=FALSE) # Get max binding energy row print(carbon_df[which.max(carbon_df$"B/A"),], row.names=FALSE) +plot(carbon_df$A, carbon_df$"B/A", xlab="Number of Nucleons", ylab="Binding Energy", main="Number of Nucleons on Binding Energy") + ## Part D: find the value of A that gives the maximum binding energy -computeMaxBind <- function(Z, precision=NA){ - if (is.na(precision)){precision <- 4} +computeMaxBind <- function(Z){ maxBind <- -Inf A.maxBind <- -Inf for (i in seq(Z, 3*Z)){ @@ -51,7 +52,16 @@ computeMaxBind <- function(Z, precision=NA){ A.maxBind <- i } } - return(c(paste("Energy: ", round(maxBind, precision), "MeV"), paste("Nucleons: ", A.maxBind))) + return(c(A.maxBind, maxBind)) } -## Part E: for each Z use the A that maximizes E/A \ No newline at end of file +## Part E: for each Z use the A that maximizes E/A +bounds <- 100 +binding_df <- data.frame(nrow=bounds, ncol=2) +for (i in seq(1, bounds)){ + # +1 since R indexes at 1 + binding_df[i,] <- c(i, computeMaxBind(i)[2]) +} + +plot(binding_df, xlab="Atomic Number", ylab="B/A [MeV]", type="o", + main="Maximum Binding Energy for Most Stable Isotopes of Each Atom")