Commit 9f570a9b authored by Stefan Gehr's avatar Stefan Gehr
Browse files

Blatt 1 Aufgabe 1

parent bc37daa5
Pipeline #50849 passed with stage
in 18 seconds
src/*
!src/*.tex
!src/*.py
!src/*.bib
build
stages:
- build
compile_pdf:
image: aergus/latex
script:
- make all
stage: build
artifacts:
expire_in: 1 week
paths:
- "build/blatt*.pdf"
.PHONY: all clean
submissionsSRC := $(wildcard src/blatt*.tex)
submissionsTARGET := $(subst .tex,.pdf,$(subst src/,build/,$(submissionsSRC)))
all: $(submissionsTARGET)
show%: build/blatt%.pdf
xdg-open $<
build:
mkdir -p build
build/blatt%.pdf: src/blatt%.tex build
latexmk -pdf -output-directory=build $<
clean:
rm -rf build
find src/ ! -name src ! -name *.tex ! -name *.bib ! -name *.py -exec rm -rf {} +
\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage[style=iso]{datetime2}
\usepackage{amsmath, amssymb}
\usepackage{hyperref}
\usepackage[separate-uncertainty=true, locale=DE]{siunitx}
\usepackage{physics}
\pdfsuppresswarningpagegroup=1
\title{Lösung EP-5 Übungsblatt}
\subtitle{Übungsblatt 1}
\author{Stefan Gehr}
\renewcommand{\thesubsection}{\thesection.\alph{subsection}}
\date{\today}
\begin{document}
\maketitle
\section{Einheiten in der Teilchenphysik}
\subsection{}
\begin{align*}
M_{\mathrm{n}}c^2
&= \SI{1.675e-27}{\kilo\gram} \cdot c^2
= \SI{1.5054149243841693e-10}{\joule} \\
&= \SI{939606091.1372457}{\electronvolt}
\approx \SI{939.6}{\mega\electronvolt} \\
m_{\mathrm{e}}c^2
&= \SI{9.109e-31}{\kilo\gram} \cdot c^2
= \SI{8.18676092311367e-14}{\joule} \\
&= \SI{510977.42592054745}{\electronvolt}
\approx \SI{0.5110}{\mega\electronvolt}
.\end{align*}
\subsection{}
Laut Wikipedia lautet die Formel
\begin{align*}
\expval{E_{\mathrm{kin}}}
&= \frac{3}{2}k_BT
= \frac{3}{2}k_B \cdot \SI{18}{\celsius}
= \frac{3}{2}k_B \cdot \SI{291.15}{\kelvin}
= \SI{0.03763404868910353}{\electronvolt} \\
&\approx \SI{0.038}{\electronvolt}
.\end{align*}
\subsection{}
\begin{align*}
\frac{hc}{\lambda} &= E_{\mathrm{Ph}} = E_{\mathrm{B}} \\
\Leftrightarrow \lambda &= \frac{hc}{E_{\mathrm{B}}}
= \frac{hc}{\SI{13.6}{\electronvolt}}
= \SI{9.116485178911785e-08}{\metre}
\approx \SI{9.12e-08}{\metre}
.\end{align*}
\subsection{}
\begin{align*}
E_{\mathrm{Ph}} &= \frac{hc}{\lambda} \\
\Leftrightarrow \lambda &= \frac{hc}{E_{\mathrm{Ph}}}
\overset{!}{<} \SI{1e-15}{\metre} \\
\Rightarrow E_{\mathrm{Ph}} &> \frac{hc}{\SI{1e-15}{\metre}}
= \SI{1.9864458571489284e-10}{\joule}
\approx \SI{1.2}{\giga\electronvolt}
.\end{align*}
\end{document}
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