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Format isotopes

Source: vignettes/articles/format_isotopes.Rmd
format_isotopes.Rmd
hyphenated notation nuclear notation nuclear notation (optional)
\mathrm{C}–\mathrm{12} \mathrm{^{12}C} \mathrm{^{12}_{6}C}
\mathrm{Fe}–\mathrm{54} \mathrm{^{54}Fe} \mathrm{^{54}_{26}Fe}
\mathrm{U}–\mathrm{238} \mathrm{^{238}U} \mathrm{^{238}_{92}U}

In this vignette, I discuss the format_nucl() function for converting isotopes from hyphenated notation to nuclear notation.

Types of notation

In hyphenated notation, chemical elements are expressed,

\mathrm{E}{-}\mathrm{A},

where E is the element symbol and A is its mass number, e.g., H-1, H-2, He-3, He-4, etc.

In nuclear notation, the element symbol has a preceding superscript for the mass number and (optionally) a preceding subscript for the atomic number Z,

\mathrm{^{A}E}\ \ \mathrm{or}\ \mathrm{^{A}_{Z}E}

For example, carbon-12 (atomic number Z = 6), iron-54 (Z = 54) and uranium-238 (Z = 92) are typeset with and without atomic numbers as shown in the table at the top of the page. The notation without Z is the default in formatdown.

Packages.   If you are writing your own script to follow along, we use the following packages in this vignette. Data frame operations are performed with data.table syntax. Some users may wish to translate the examples to use base R or dplyr syntax.

Markup

We format isotopes as inline math expressions delimited by $ ... $ or the optional $ ... $. For example, carbon 12 is marked up as

    $\mathrm{^{12}C}$,

where the \mathrm{} macro creates serif, non-italic text and the carat ^{} creates the superscript for the mass number. Rendering this expression in an Rmd script as a LaTeX-style inline equation yields: \mathrm{^{\small\ 12}C}.

To program the markup, however, we enclose it in quote marks as a character string, that is,

    "$\\mathrm{^{12}C}$",

which requires us to “escape” the backslash in \mathrm by adding extra backslashes. Rendering this expression in an Rmd script as an inline R code chunk yields the same result: \mathrm{^{12}C}.

format_nucl()

Denoting E as the element symbol (H, He, Li, Be, …) and A as the mass number of its isotope, format_nucl() converts a string from the hyphenated text form,

    "E-A"

to a character string in the markup form,

    "$\\mathrm{^{A}E}$",

If the option for including the atomic number Z is used, the markup form includes the atomic number as a subscript using the underscore macro _{},

    "$\\mathrm{^{A}_{Z}E}$".


Usage.  

format_nucl(x,
            face  = "plain",
            ...,
            Z     = formatdown_options("Z"),
            warn = formatdown_options("warn"),
            delim = formatdown_options("delim"))
  • Arguments before the dots do not have to be named if argument order is maintained. Arguments after the dots (...) must be named.
  • The arguments assigned via formatdown_options() can be reset by the user locally in a function call or globally using formatdown_options().
  • Returns a vector


Examples.   Scalar values are typically rendered using inline code chunks in an Rmd script.

# 1. Carbon-12
x <- "C-12"
format_nucl(x)
#> [1] "$\\mathrm{^{12}C}$"

# 2. Uranium-238
y <- "U-238"
format_nucl(y)
#> [1] "$\\mathrm{^{238}U}$"

Examples 1 and 2 (in inline code chunks) render as,

  1. \mathrm{^{12}C} is the most abundant isotope of carbon.

  2. The most common isotope of naturally-occurring uranium is \mathrm{^{238}U}.


Including the atomic numbers

To include the atomic number (automatically obtained from a built-in data set), we can set the optional Z argument to TRUE.


Examples.  

# 3. Carbon-12
x <- "C-12"
format_nucl(x, Z = TRUE)
#> [1] "$\\mathrm{^{12}_{6}C}$"

# 4. Uranium-238
y <- "U-238"
format_nucl(y, Z = TRUE)
#> [1] "$\\mathrm{^{238}_{92}U}$"

Examples 3 and 4 (in inline code chunks) render as,

  1. \mathrm{^{12}_{6}C} is the most abundant isotope of carbon.

  2. The most common isotope of naturally-occurring uranium is \mathrm{^{238}_{92}U}.


The Z argument can also be set globally using formatdown_options(), saving the effort of using the Z argument in every function call.

formatdown_options(Z = TRUE)

# 5. Carbon-12
format_nucl(x)
#> [1] "$\\mathrm{^{12}_{6}C}$"

# 6. Uranium-238
format_nucl(y)
#> [1] "$\\mathrm{^{238}_{92}U}$"

Examples 5 and 6 (in inline code chunks) render as,

  1. \mathrm{^{12}_{6}C} is the most abundant isotope of carbon.

  2. The most common isotope of naturally-occurring uranium is \mathrm{^{238}_{92}U}.


To reset the default option,

# reset the Z option only
formatdown_options(Z = FALSE)

Typeface

Format the same column of text using each of the five possible face arguments for comparison.

# 7. Compare available typefaces
x <- c("He-4", "C-12", "Pb-204", "U-238")
plain <- format_nucl(x, face = "plain", Z = TRUE)
italic <- format_nucl(x, face = "italic", Z = TRUE)
bold <- format_nucl(x, face = "bold", Z = TRUE)
sans <- format_nucl(x, face = "sans", Z = TRUE)
mono <- format_nucl(x, face = "mono", Z = TRUE)
DT <- data.table(plain, italic, bold, sans, mono)
knitr::kable(DT, align = "l", caption = "Example 7.")
Example 7.
plain italic bold sans mono
\mathrm{^{4}_{2}He} \mathit{^{4}_{2}He} \mathbf{^{4}_{2}He} \mathsf{^{4}_{2}He} \mathtt{^{4}_{2}He}
\mathrm{^{12}_{6}C} \mathit{^{12}_{6}C} \mathbf{^{12}_{6}C} \mathsf{^{12}_{6}C} \mathtt{^{12}_{6}C}
\mathrm{^{204}_{82}Pb} \mathit{^{204}_{82}Pb} \mathbf{^{204}_{82}Pb} \mathsf{^{204}_{82}Pb} \mathtt{^{204}_{82}Pb}
\mathrm{^{238}_{92}U} \mathit{^{238}_{92}U} \mathbf{^{238}_{92}U} \mathsf{^{238}_{92}U} \mathtt{^{238}_{92}U}

Element data set

The package includes a data set of the 118 chemical elements with columns for the element name, symbol, atomic number, and mass number. Because elements may have more than one isotope with distinct mass numbers, we list each isotope in its own row, resulting in a data frame with 354 rows.

element_set
#>          element symbol atomic_number mass_number
#>           <char> <char>        <char>      <char>
#>   1:    Hydrogen      H             1           1
#>   2:    Hydrogen      H             1           2
#>   3:    Hydrogen      H             1           3
#>  ---                                             
#> 352: Livermorium     Lv           116         293
#> 353:  Tennessine     Ts           117         292
#> 354:   Oganesson     Og           118         294

View the help page for the data set by typing

    library("formatdown")  
    ? element_set

Examples.   For example, the three isotopes of hydrogen are expressed,

# 8. Hydrogen isotopes
x <- c("H-1", "H-2", "H-3")
format_nucl(x, Z = TRUE)
#> [1] "$\\mathrm{^{1}_{1}H}$" "$\\mathrm{^{2}_{1}H}$" "$\\mathrm{^{3}_{1}H}$"

Example 8 renders as: \mathrm{^{1}_{1}H}, \mathrm{^{2}_{1}H}, \mathrm{^{3}_{1}H}


Warning of input errors.   The data set of isotopes is also used to warn of the following input errors:

  • hyphenated input symbol fails to match a standard element symbol
  • hyphenated mass number fails to match a known isotope

Examples.  

Here, the first entry has an incorrect element symbol and the second has an incorrect mass number.

# 9. Input errors
x <- c("Carbon-12", "C-40", "C-12")
format_nucl(x)
#> Warning in format_nucl(x): Incorrect chemical symbol or mass number in
#> c("Carbon-12", "C-40")
#> [1] "$\\mathrm{^{12}Carbon}$" "$\\mathrm{^{40}C}$"     
#> [3] "$\\mathrm{^{12}C}$"

Example 9 renders as \mathrm{^{12}Carbon}, \mathrm{^{40}C}, \mathrm{^{12}C}

If we use the atomic number argument, the letter Z is placed in the subscript.

# 10. Symbol for atomic number
format_nucl(x, Z = TRUE)
#> Warning in format_nucl(x, Z = TRUE): Incorrect chemical symbol or mass number
#> in c("Carbon-12", "C-40")
#> [1] "$\\mathrm{^{12}_{Z}Carbon}$" "$\\mathrm{^{40}_{Z}C}$"     
#> [3] "$\\mathrm{^{12}_{6}C}$"

Example 10 renders as \mathrm{^{12}_{Z}Carbon}, \mathrm{^{40}_{Z}C}, \mathrm{^{12}_{6}C}

The third entry of the output vector is correctly formatted. The “Z” subscript in the other two entries is a hint (in addition to the warning) that the hyphenated input contains errors.


Notating a general form.   That an unrecognized input in hyphenated form is still formatted allows us to create a nuclear notation is general form. In such a case, we can turn off the warning using the warn argument.

Examples.  

# 11. General nuclear form
x <- c("E-A")
format_nucl(x, warn = FALSE)
#> [1] "$\\mathrm{^{A}E}$"

Example 11 renders as: \mathrm{^{A}E}

As noted earlier, the usual Z argument in this case places a Z in the subscript position.

# 12. General nuclear form with atomic number symbol
x <- c("E-A")
format_nucl(x, Z = TRUE, warn = FALSE)
#> [1] "$\\mathrm{^{A}_{Z}E}$"

Example 12 renders as: \mathrm{^{A}_{Z}E}

Some authors prefer using X for the general element symbol,

# 13. Alternate general form.
x <- c("X-A")
format_nucl(x, Z = TRUE, warn = FALSE)
#> [1] "$\\mathrm{^{A}_{Z}X}$"

Example 13 renders as: \mathrm{^{A}_{Z}X}

Inputs

Scalars.   Generally used with inline R code. For example, the following R markdown sentence, which includes some inline R code,

    The most common isotope of Germanium is `r format_nucl("Ge-74")` with a
    naturally occurring frequency of 36% though `r format_nucl("Ge-72")` is
    a close second at 28%.

renders as:

The most common isotope of Germanium is \mathrm{^{74}Ge} with a naturally occurring frequency of 36% though \mathrm{^{72}Ge} is a close second at 28%.


Vector.   A vector of isotopes in hyphenated form (or a data frame column) is marked up as follows,

Examples.  

# 14. Sample vector
x <- c("H-1", "H-2", "He-3", "He-4", "Li-6", "Li-7", "Be-9")
format_nucl(x)
#> [1] "$\\mathrm{^{1}H}$"  "$\\mathrm{^{2}H}$"  "$\\mathrm{^{3}He}$"
#> [4] "$\\mathrm{^{4}He}$" "$\\mathrm{^{6}Li}$" "$\\mathrm{^{7}Li}$"
#> [7] "$\\mathrm{^{9}Be}$"

In a table, the output can be rendered as,

DT <- data.table(x, format_nucl(x))
knitr::kable(DT,
  align = "c",
  col.names = c("Hyphenated form", "Nuclear notation"),
  caption = "Example 14."
)
Example 14.
Hyphenated form Nuclear notation
H-1 \mathrm{^{1}H}
H-2 \mathrm{^{2}H}
He-3 \mathrm{^{3}He}
He-4 \mathrm{^{4}He}
Li-6 \mathrm{^{6}Li}
Li-7 \mathrm{^{7}Li}
Be-9 \mathrm{^{9}Be}


Adding atomic numbers yields,

# 15. Table with Z
DT <- data.table(x, format_nucl(x, Z = TRUE))
knitr::kable(DT,
  align = "c",
  col.names = c("Hyphenated form", "Nuclear notation"),
  caption = "Example 15."
)
Example 15.
Hyphenated form Nuclear notation
H-1 \mathrm{^{1}_{1}H}
H-2 \mathrm{^{2}_{1}H}
He-3 \mathrm{^{3}_{2}He}
He-4 \mathrm{^{4}_{2}He}
Li-6 \mathrm{^{6}_{3}Li}
Li-7 \mathrm{^{7}_{3}Li}
Be-9 \mathrm{^{9}_{4}Be}


Options

Arguments assigned using formatdown_options() are described in the Global settings article.