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\textcolor{spec}{\texttt{#1}}\fi} +\newcommand{\FmtWP}[2]{\ifnum#2>0 \textcolor{wpU}{\texttt{#1}}\else \textcolor{wp}{\texttt{#1}}\fi} +\newcommand{\FmtWO}[2]{\ifnum#2>0 \textcolor{woU}{\texttt{#1}}\else \textcolor{wo}{\texttt{#1}}\fi} +% Increment commands +\renewcommand{\markSpec}[1]{% + \stepcounter{SpecCntpg}% + \addtocounter{SpecCount#1}{1}% + \addtocounter{GlobalSpecCount#1}{1}} +\renewcommand{\markWP}[1]{% + \stepcounter{WPCntpg}% + \addtocounter{WPCount#1}{1}% + \addtocounter{GlobalWPCount#1}{1}} +\renewcommand{\markWO}[1]{% + \stepcounter{WOCntpg}% + \addtocounter{WOCount#1}{1}% + \addtocounter{GlobalWOCount#1}{1}} +\makeatother +\AddToHook{shipout/after}{\foreach \c in {SpecCount10.1,SpecCount10.2,SpecCount10.3,SpecCount10.4,SpecCount10.5,SpecCount10.6,SpecCount10.7,SpecCount10.8,WOCount1,WOCount2,WOCount3,WOCount4,WOCount5,WPCount1.1,WPCount1.2,WPCount1.3,WPCount1.4,WPCount1.5,WPCount1.6,WPCount1.7,WPCount1.8,WPCount1.9,WPCount1.10,WPCount1.11,WPCount1.12,WPCount1.13,WPCount1.14,WPCount1.15,WPCount1.17,WPCount1.18,WPCount1.19,WPCount1.20}{\setcounter{\c}{0}}\global\setcounter{SpecCntpg}{0}\global\setcounter{WPCntpg}{0}\global\setcounter{WOCntpg}{0}} + +% % === Creating the tree in the right margin === +% \newcommand{\Tree}[3]{\markSpec{#1}% +% \marginpar{\scriptsize +% \begin{itemize}[leftmargin=0pt,label={}] +% \item \ok\;\hyperlink{ws-#1}{\FmtSpec{WS #1}{\getRawCount{SpecCount#1}}} +% \begin{itemize}[leftmargin=1.2em,label={}] +% #2 #3 +% \end{itemize} +% \end{itemize}}} + + % === Creating the tree in the right margin === +\newcommand{\Tree}[3]{\markSpec{#1}% +\marginpar{\parbox{2.5cm}{\scriptsize\raggedright + \begin{itemize}[leftmargin=0pt,label={}] + \item \ok\;\hyperlink{ws-#1}{\mbox{\FmtSpec{WS #1}{\getRawCount{SpecCount#1}}}} + \begin{itemize}[leftmargin=1.2em,label={}] + #2 #3 + \end{itemize} + \end{itemize}}}} + +% === WO and WP items === +\newcommand{\WOitem}[1]{\markWO{#1}\item \nok\;\hyperlink{wo-#1}{\FmtWO{WO 0#1.00}{\getRawCount{WOCount#1}}}} +\newcommand{\WOitemSol}[1]{\markWO{#1}\item \ok\;\hyperlink{wo-#1}{\FmtWO{WO 0#1.00}{\getRawCount{WOCount#1}}}} +\newcommand{\WPItem}[1]{\markWP{#1}\item \nok\;\hyperlink{wp-#1}{\FmtWP{WP #1}{\getRawCount{WPCount#1}}}} +\newcommand{\WPItemSol}[1]{\markWP{#1}\item \ok\;\hyperlink{wp-#1}{\FmtWP{WP #1}{\getRawCount{WPCount#1}}}} + +% === Separator for stages === +\newcommand{\EtapLine}{\par\noindent\rule{\linewidth}{0.4pt}\par\noindent} + +% === Header and Footer === +\pagestyle{fancy} +\fancyhf{} +\lhead{2024M10 Fizyka Atomowa (PP(R-10))} +\chead{\thepage} +\rhead{M. Pabiszczak, Słubice \today} +\fancyfoot[L]{% + \tiny + \begin{tabular}{p{2.5em} *{8}{p{5em}}} + \textcolor{spec}{\textbf{WS:}} & \hyperlink{ws-10.1}{\FmtSpec{10.01}{\getRawCount{SpecCount10.1}}}[{\getSpecCount{SpecCount10.1}}] & \hyperlink{ws-10.2}{\FmtSpec{10.02}{\getRawCount{SpecCount10.2}}}[{\getSpecCount{SpecCount10.2}}] & \hyperlink{ws-10.3}{\FmtSpec{10.03}{\getRawCount{SpecCount10.3}}}[{\getSpecCount{SpecCount10.3}}] & \hyperlink{ws-10.4}{\FmtSpec{10.04}{\getRawCount{SpecCount10.4}}}[{\getSpecCount{SpecCount10.4}}] & \hyperlink{ws-10.5}{\FmtSpec{10.05}{\getRawCount{SpecCount10.5}}}[{\getSpecCount{SpecCount10.5}}] & \hyperlink{ws-10.6}{\FmtSpec{10.06}{\getRawCount{SpecCount10.6}}}[{\getSpecCount{SpecCount10.6}}] & \hyperlink{ws-10.7}{\FmtSpec{10.07}{\getRawCount{SpecCount10.7}}}[{\getSpecCount{SpecCount10.7}}] & \hyperlink{ws-10.8}{\FmtSpec{10.08}{\getRawCount{SpecCount10.8}}}[{\getSpecCount{SpecCount10.8}}] \\ + \textcolor{wo}{\textbf{WO:}} & \hyperlink{wo-1}{\FmtWO{01.00}{\getRawCount{WOCount1}}}[{\getWOCount{WOCount1}}] & \hyperlink{wo-2}{\FmtWO{02.00}{\getRawCount{WOCount2}}}[{\getWOCount{WOCount2}}] & \hyperlink{wo-3}{\FmtWO{03.00}{\getRawCount{WOCount3}}}[{\getWOCount{WOCount3}}] & \hyperlink{wo-4}{\FmtWO{04.00}{\getRawCount{WOCount4}}}[{\getWOCount{WOCount4}}] & \hyperlink{wo-5}{\FmtWO{05.00}{\getRawCount{WOCount5}}}[{\getWOCount{WOCount5}}] & & & \\ + \textcolor{wp}{\textbf{WP:}} & \hyperlink{wp-1.1}{\FmtWP{01.01}{\getRawCount{WPCount1.1}}}[{\getWPCount{WPCount1.1}}] & \hyperlink{wp-1.2}{\FmtWP{01.02}{\getRawCount{WPCount1.2}}}[{\getWPCount{WPCount1.2}}] & \hyperlink{wp-1.3}{\FmtWP{01.03}{\getRawCount{WPCount1.3}}}[{\getWPCount{WPCount1.3}}] & \hyperlink{wp-1.4}{\FmtWP{01.04}{\getRawCount{WPCount1.4}}}[{\getWPCount{WPCount1.4}}] & \hyperlink{wp-1.5}{\FmtWP{01.05}{\getRawCount{WPCount1.5}}}[{\getWPCount{WPCount1.5}}] & \hyperlink{wp-1.6}{\FmtWP{01.06}{\getRawCount{WPCount1.6}}}[{\getWPCount{WPCount1.6}}] & \hyperlink{wp-1.7}{\FmtWP{01.07}{\getRawCount{WPCount1.7}}}[{\getWPCount{WPCount1.7}}] & \hyperlink{wp-1.8}{\FmtWP{01.08}{\getRawCount{WPCount1.8}}}[{\getWPCount{WPCount1.8}}] \\ + & \hyperlink{wp-1.9}{\FmtWP{01.09}{\getRawCount{WPCount1.9}}}[{\getWPCount{WPCount1.9}}] & \hyperlink{wp-1.10}{\FmtWP{01.10}{\getRawCount{WPCount1.10}}}[{\getWPCount{WPCount1.10}}] & \hyperlink{wp-1.11}{\FmtWP{01.11}{\getRawCount{WPCount1.11}}}[{\getWPCount{WPCount1.11}}] & \hyperlink{wp-1.12}{\FmtWP{01.12}{\getRawCount{WPCount1.12}}}[{\getWPCount{WPCount1.12}}] & \hyperlink{wp-1.13}{\FmtWP{01.13}{\getRawCount{WPCount1.13}}}[{\getWPCount{WPCount1.13}}] & \hyperlink{wp-1.14}{\FmtWP{01.14}{\getRawCount{WPCount1.14}}}[{\getWPCount{WPCount1.14}}] & \hyperlink{wp-1.15}{\FmtWP{01.15}{\getRawCount{WPCount1.15}}}[{\getWPCount{WPCount1.15}}] & \hyperlink{wp-1.17}{\FmtWP{01.17}{\getRawCount{WPCount1.17}}}[{\getWPCount{WPCount1.17}}] \\ + & \hyperlink{wp-1.18}{\FmtWP{01.18}{\getRawCount{WPCount1.18}}}[{\getWPCount{WPCount1.18}}] & \hyperlink{wp-1.19}{\FmtWP{01.19}{\getRawCount{WPCount1.19}}}[{\getWPCount{WPCount1.19}}] & \hyperlink{wp-1.20}{\FmtWP{01.20}{\getRawCount{WPCount1.20}}}[{\getWPCount{WPCount1.20}}] & & & & & \\ + \end{tabular} \\ + \vspace{4pt} + \hrule + \vspace{4pt} + \textbf{Realizacja:} \textcolor{spec}{WS działu} \the\numexpr(\getRawCount{SpecCount10.1}+\getRawCount{SpecCount10.2}+\getRawCount{SpecCount10.3}+\getRawCount{SpecCount10.4}+\getRawCount{SpecCount10.5}+\getRawCount{SpecCount10.6}+\getRawCount{SpecCount10.7}+\getRawCount{SpecCount10.8})*100/8\relax\% (\the\numexpr\getRawCount{SpecCount10.1}+\getRawCount{SpecCount10.2}+\getRawCount{SpecCount10.3}+\getRawCount{SpecCount10.4}+\getRawCount{SpecCount10.5}+\getRawCount{SpecCount10.6}+\getRawCount{SpecCount10.7}+\getRawCount{SpecCount10.8}\relax/8) | \textcolor{wo}{WO ogólnych} \the\numexpr(\getRawCount{WOCount1}+\getRawCount{WOCount2}+\getRawCount{WOCount3}+\getRawCount{WOCount4}+\getRawCount{WOCount5})*100/5\relax\% (\the\numexpr\getRawCount{WOCount1}+\getRawCount{WOCount2}+\getRawCount{WOCount3}+\getRawCount{WOCount4}+\getRawCount{WOCount5}\relax/5) | \textcolor{wp}{WP przekrojowych} \the\numexpr(\getRawCount{WPCount1.1}+\getRawCount{WPCount1.2}+\getRawCount{WPCount1.3}+\getRawCount{WPCount1.4}+\getRawCount{WPCount1.5}+\getRawCount{WPCount1.6}+\getRawCount{WPCount1.7}+\getRawCount{WPCount1.8}+\getRawCount{WPCount1.9}+\getRawCount{WPCount1.10}+\getRawCount{WPCount1.11}+\getRawCount{WPCount1.12}+\getRawCount{WPCount1.13}+\getRawCount{WPCount1.14}+\getRawCount{WPCount1.15}+\getRawCount{WPCount1.17}+\getRawCount{WPCount1.18}+\getRawCount{WPCount1.19}+\getRawCount{WPCount1.20})*100/20\relax\% (\the\numexpr\getRawCount{WPCount1.1}+\getRawCount{WPCount1.2}+\getRawCount{WPCount1.3}+\getRawCount{WPCount1.4}+\getRawCount{WPCount1.5}+\getRawCount{WPCount1.6}+\getRawCount{WPCount1.7}+\getRawCount{WPCount1.8}+\getRawCount{WPCount1.9}+\getRawCount{WPCount1.10}+\getRawCount{WPCount1.11}+\getRawCount{WPCount1.12}+\getRawCount{WPCount1.13}+\getRawCount{WPCount1.14}+\getRawCount{WPCount1.15}+\getRawCount{WPCount1.17}+\getRawCount{WPCount1.18}+\getRawCount{WPCount1.19}+\getRawCount{WPCount1.20}\relax/20) +} + +% === Defining WO and WP descriptions === +\def\DescWO#1{\ifnum#1=1 Wykorzystanie pojęć i wielkości fizycznych do opisu zjawisk oraz wskazywanie ich przykładów w otaczającej rzeczywistości.\fi + \ifnum#1=2 Rozwiązywanie problemów z wykorzystaniem praw i zależności fizycznych.\fi + \ifnum#1=3 Planowanie i przeprowadzanie obserwacji oraz doświadczeń i wnioskowanie na podstawie ich wyników.\fi + \ifnum#1=4 Posługiwanie się informacjami pochodzącymi z analizy materiałów źródłowych, w tym tekstów popularnonaukowych i źródeł internetowych, oraz ocenianie wiarygodności źródeł.\fi + \ifnum#1=5 Budowanie modeli fizycznych i matematycznych do opisu zjawisk oraz ilustracji praw i zależności fizycznych.\fi} +\def\DescWP#1{\ifnum#1=1.1 Przedstawia jednostki wielkości fizycznych, wyraża je poprzez jednostki podstawowe; przelicza wielokrotności i podwielokrotności.\fi + \ifnum#1=1.2 Posługuje się materiałami pomocniczymi, w tym tablicami fizycznymi i chemicznymi oraz kartą wybranych wzorów i stałych fizykochemicznych.\fi + \ifnum#1=1.3 Prowadzi obliczenia szacunkowe i poddaje analizie otrzymany wynik.\fi + \ifnum#1=1.4 Przeprowadza obliczenia liczbowe, posługując się kalkulatorem.\fi + \ifnum#1=1.5 Rozróżnia wielkości wektorowe i skalarne, wykonuje graficznie działania na wektorach (dodawanie, odejmowanie, mnożenie przez liczbę, rozkładanie na składowe).\fi + \ifnum#1=1.6 Tworzy teksty, tabele, diagramy lub wykresy, rysunki schematyczne lub blokowe dla zilustrowania zjawisk bądź problemu; właściwie skaluje, oznacza i dobiera zakresy osi.\fi + \ifnum#1=1.7 Wyodrębnia z tekstów, tabel, diagramów lub wykresów, rysunków schematycznych lub blokowych informacje kluczowe dla opisywanego zjawiska bądź problemu; przedstawia te informacje w różnych postaciach.\fi + \ifnum#1=1.8 Rozpoznaje zależność rosnącą bądź malejącą na podstawie danych z tabeli lub na podstawie wykresu; rozpoznaje proporcjonalność prostą na podstawie wykresu.\fi + \ifnum#1=1.9 Dopasowuje prostą do danych przedstawionych w postaci wykresu; interpretuje nachylenie tej prostej i punkty przecięcia z osiami.\fi + \ifnum#1=1.10 Przeprowadza wybrane obserwacje, pomiary i doświadczenia na podstawie ich opisów; planuje i modyfikuje ich przebieg; formułuje hipotezę i prezentuje kroki niezbędne do jej weryfikacji.\fi + \ifnum#1=1.11 Opisuje przebieg doświadczenia lub pokazu; wyróżnia kluczowe kroki i sposób postępowania oraz wskazuje rolę użytych przyrządów i uwzględnia ich rozdzielczość.\fi + \ifnum#1=1.12 Przestrzega zasad bezpieczeństwa podczas wykonywania obserwacji, pomiarów i doświadczeń.\fi + \ifnum#1=1.13 Wyznacza średnią z kilku pomiarów jako końcowy wynik pomiaru powtarzanego.\fi + \ifnum#1=1.14 Posługuje się pojęciem niepewności pomiaru wielkości prostych; zapisuje wynik pomiaru wraz z jego jednostką oraz z uwzględnieniem informacji o niepewności; uwzględnia niepewności przy sporządzaniu wykresów.\fi + \ifnum#1=1.15 Przeprowadza obliczenia i zapisuje wynik zaokrąglony do zadanej liczby cyfr znaczących.\fi + \ifnum#1=1.17 Przedstawia własnymi słowami główne tezy tekstu popularnonaukowego z dziedziny fizyki lub astronomii.\fi + \ifnum#1=1.18 Wyodrębnia zjawisko z kontekstu, nazywa je oraz wskazuje czynniki istotne i nieistotne dla jego przebiegu.\fi + \ifnum#1=1.19 Tworzy modele fizyczne lub matematyczne wybranych zjawisk i opisuje ich założenia; ilustruje prawa i zależności fizyczne z wykorzystaniem tych założeń.\fi + \ifnum#1=1.20 Posługuje się pojęciami pracy, mocy, energii kinetycznej; wykorzystuje równość między pracą siły wypadkowej i zmianą energii kinetycznej oraz zasadę zachowania energii mechanicznej do obliczeń.\fi} +\def\DescWS#1{\ifnum#1=10.1 Analizuje na wybranych przykładach promieniowanie termiczne ciał i jego zależność od temperatury.\fi + \ifnum#1=10.2 Opisuje dualizm korpuskularno-falowy światła; posługuje się pojęciem fotonu oraz oblicza jego energię.\fi + \ifnum#1=10.3 Rozróżnia widma emisyjne i absorpcyjne gazów; interpretuje linie widmowe jako skutek przejść między poziomami energetycznymi w atomach z emisją lub absorpcją kwantu światła; rozróżnia stan podstawowy i stany wzbudzone atomu.\fi + \ifnum#1=10.4 Analizuje seryjny układ linii widmowych na przykładzie widma atomu wodoru; oblicza różnice energii między poziomami energetycznymi w atomie wodoru.\fi + \ifnum#1=10.5 Posługuje się pojęciem pędu fotonu; stosuje zasadę zachowania energii i zasadę zachowania pędu do opisu emisji i absorpcji przez swobodne atomy; opisuje odrzut atomu emitującego kwant światła.\fi + \ifnum#1=10.6 Opisuje zjawiska jonizacji i fotoelektryczne jako wywołane tylko przez promieniowanie o częstotliwości większej od granicznej.\fi + \ifnum#1=10.7 Opisuje zjawiska dyfrakcji oraz interferencji elektronów i innych cząstek; oblicza długość fali de Broglie’a poruszających się cząstek.\fi + \ifnum#1=10.8 Doświadczalnie: obserwuje widma atomowe za pomocą siatki dyfrakcyjnej.\fi} + +% ==================== Document Body ========================================== +\begin{document} + +\section*{Treść zadania: Ark. Fiz. Maj 2024, Zad. 10} +\noindent\begin{minipage}{\linewidth} + \hrule height 0.4pt + \vspace{0.5em} + \noindent + Elektron został rozpędzony w polu elektrycznym (w próżni) od punktu $A$ do punktu~$B$. + Wartość prędkości elektronu w punkcie $A$ była równa zero, a wartość prędkości elektronu w punkcie $B$ była równa: + + \begin{equation} + v = 2.00 \times 10^8 \, \text{m/s}. + \label{eq:predkosc} + \end{equation} + + Przyjmij, że: + \begin{enumerate} + \item Energia spoczynkowa elektronu dana jest wzorem: + \begin{equation} + E_0 \approx 5.11 \times 10^5 \, \text{eV}, + \label{eq:energia_spoczynkowa} + \end{equation} + \item Całkowita energia elektronu w punkcie $B$ oznaczona jest jako $E_B$. + \item Gotów jesteś do rozwiązania zadania. + \end{enumerate} + \vspace{0.5em} + \hrule height 0.4pt +\end{minipage} + +\clearpage +\textbf{10.1}\;Dokończ zadanie. Wpisz właściwą liczbę w wydzielone miejsce. \\ +Ilość energii \( \frac{E_B}{E_0} \) jest równa (w zaokrągleniu) \fbox{ \phantom{0.00} } \\ +\Tree{10.3}{\WOitemSol{2}\WOitemSol{5}} + +\vspace{0.1em} +\hrule +\vspace{0.1em} +Brudnopis \\ +\begin{tikzpicture} + \draw[step=0.5cm,gray,very thin] (0,0) grid (\linewidth,16); +\end{tikzpicture} \\ + +\vspace{0.1em} +\hrule +\vspace{-0.1em} + +\vspace*{\fill} + +\begin{tabular}{|p{0.5\textwidth}|p{0.15\textwidth}|p{0.15\textwidth}|} + \hline + \textbf{Uzasadnienie} & \textbf{Pkt. Max} & \textbf{Pkt. zdobyte za zadanie} \\ + \hline + \scriptsize Punktacja: WS 10.3 (1 pkt) × WO 2 (1 pkt) + WS 10.3 (1 pkt) × WO 5 (1 pkt) = $1 \times 1 + 1 \times 1 = 2$ pkt. & 2 & 2 \\ + \hline +\end{tabular} + +\vspace{1em} +\hrule + +% ---------- Task 10.1 Solution ---------------------------------------------- +\clearpage +\section*{Zadanie 10.1} +\subsection*{Etap 1 – Stosunek energii \( \frac{E_B}{E_0} \)} +\EtapLine +\Tree{10.3}{\WOitemSol{2}\WOitemSol{5}} + +Aby obliczyć stosunek energii całkowitej \( E_B \) do energii spoczynkowej \( E_0 \), korzystamy z wzoru na energię całkowitą: + +\marginpar{ +\item \scriptsize Tablice: + \begin{itemize}[leftmargin=1.2em,label={}] + \item s. 19: + \begin{itemize}[leftmargin=1.2em,label={}] + \item \href{https://cke.gov.pl/images/_EGZAMIN_MATURALNY_OD_2023/Informatory/wybrane_wzory_stale_fizykochemiczne_EM2023.pdf}{eq 1} + \item \href{https://cke.gov.pl/images/_EGZAMIN_MATURALNY_OD_2023/Informatory/wybrane_wzory_stale_fizykochemiczne_EM2023.pdf}{eq 2} + \end{itemize} + \end{itemize}} + +\begin{equation} +E_B = \frac{E_0}{\sqrt{1 - \left(\frac{v}{c}\right)^2}} +\label{eq:total_energy_10_1} +\end{equation} + +% \marginpar{\scriptsize \href{https://cke.gov.pl/images/_EGZAMIN_MATURALNY_OD_2023/Informatory/wybrane_wzory_stale_fizykochemiczne_EM2023.pdf}{T. s19 eq 1 i 2}} + + + +Stosunek \( \frac{E_B}{E_0} \) jest równy czynnikowi Lorentza \( \gamma \): +\begin{equation} +\frac{E_B}{E_0} = \gamma = \frac{1}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}} +\label{eq:energy_ratio} +\end{equation} +Podstawiamy \( v = 2.00 \times 10^8 \, \text{m/s} \), \( c = 3.00 \times 10^8 \, \text{m/s} \): +\begin{equation} +\gamma = \frac{1}{\sqrt{1 - \left(\frac{2.00 \times 10^8}{3.00 \times 10^8}\right)^2}}} = \frac{1}{\sqrt{1 - \left(\frac{2}{3}\right)^2}}} = \frac{1}{\sqrt{1 - 0.4444}}} \approx 1.34 +\label{eq:gamma_10_1} +\end{equation} +Wynik końcowy to: +\begin{equation} +\frac{E_B}{E_0} \approx 1.34 +\label{eq:energy_ratio_final} +\end{equation} +Zatem w wykropkowane miejsce wpisujemy: +\[ +\boxed{1.34} +\] +\EtapLine +\begin{tabular}{|p{0.5\textwidth}|p{0.15\textwidth}|p{0.15\textwidth}|} + \hline + \textbf{Uzasadnienie} & \textbf{Pkt. Max} & \textbf{Pkt. zdobyte za zadanie} \\ + \hline + Punktacja: WS 10.3 (1 pkt) × WO 2 (1 pkt) + WS 10.3 (1 pkt) × WO 5 (1 pkt) = \( 1 \times 1 + 1 \times 1 = 2 \) pkt. & 2 & 2 \\ + \hline +\end{tabular} \\ +\hrule + +% ---------- Task 10.2 Content ----------------------------------------------- +\clearpage +\textbf{10.2}\;Oblicz napięcie elektryczne \( U_{AB} \) między punktami \( A \) i \( B \). Zapisz obliczenia. \\ +\Tree{10.3}{\WOitemSol{2}\WOitemSol{5}}{\WPItemSol{1.3}\WPItemSol{1.15}\WPItemSol{1.20}} +Brudnopis \\ +\begin{tikzpicture} + \draw[step=0.5cm,gray,very thin] (0,0) grid (\linewidth,12); +\end{tikzpicture} \\ +\vspace*{\fill} +\begin{tabular}{|p{0.5\textwidth}|p{0.15\textwidth}|p{0.15\textwidth}|} + \hline + \textbf{Uzasadnienie} & \textbf{Pkt. Max} & \textbf{Pkt. zdobyte za zadanie} \\ + \hline + Punktacja: WS 10.3 (1 pkt) × WO 2 (1 pkt) + WS 10.3 (1 pkt) × WO 5 (1 pkt) + WS 10.3 (1 pkt) × WP 1.20 (1 pkt) = \( 1 \times 1 + 1 \times 1 + 1 \times 1 = 3 \) pkt. & 3 & 3 \\ + \hline +\end{tabular} \\ +\hrule + +% ---------- Task 10.2 Solution ---------------------------------------------- +\clearpage +\section*{Zadanie 10.2} +\subsection*{Etap 1 – Energia kinetyczna} +\EtapLine +\Tree{10.3}{\WOitemSol{2}\WOitemSol{5}}{\WPItemSol{1.3}\WPItemSol{1.15}\WPItemSol{1.20}} +Aby obliczyć energię kinetyczną \( E_k \) elektronu w punkcie \( B \), korzystamy z wzoru na energię całkowitą: +\begin{equation} +E_B = \frac{E_0}{\sqrt{1 - \left(\frac{v}{c}\right)^2}} +\label{eq:total_energy_10_2} +\end{equation} +Czynnik Lorentza \( \gamma \approx 1.34 \). Energia całkowita \( E_B \) wynosi: +\begin{equation} +E_B = \gamma E_0 = 1.34 \times 5.11 \times 10^5 \approx 6.85 \times 10^5 \, \text{eV} +\label{eq:EB_10_2} +\end{equation} +Energia kinetyczna to różnica: +\begin{equation} +E_k = E_B - E_0 = (6.85 \times 10^5) - (5.11 \times 10^5) \approx 1.74 \times 10^5 \, \text{eV} +\label{eq:Ek_10_2} +\end{equation} +\EtapLine + +\subsection*{Etap 2 – Napięcie \( U_{AB} \)} +\EtapLine +\Tree{10.3}{\WOitemSol{2}}{\WPItemSol{1.20}} +Aby znaleźć napięcie \( U_{AB} \): +\begin{equation} +q U_{AB} = E_{kinB} +\label{eq:voltage_10_2} +\end{equation} +Zatem: +\begin{equation} +U_{AB} = \frac{E_k}{q} = 1.74 \times 10^5 \, \text{V} +\label{eq:U_AB_final_10_2} +\end{equation} +\EtapLine +\begin{tabular}{|p{0.5\textwidth}|p{0.15\textwidth}|p{0.15\textwidth}|} + \hline + \textbf{Uzasadnienie} & \textbf{Pkt. Max} & \textbf{Pkt. zdobyte za zadanie} \\ + \hline + Punktacja: WS 10.3 (1 pkt) × WO 2 (1 pkt) + WS 10.3 (1 pkt) × WO 5 (1 pkt) + WS 10.3 (1 pkt) × WP 1.20 (1 pkt) = \( 1 \times 1 + 1 \times 1 + 1 \times 1 = 3 \) pkt. & 3 & 3 \\ + \hline +\end{tabular} \\ +\hrule + +% % ---------- Summary Table ---------------------------------------------- +% \clearpage +% \section*{Podsumowanie punktacji i wymagań} +% \begin{tabular}{|p{0.15\textwidth}|p{0.15\textwidth}|p{0.15\textwidth}|p{0.15\textwidth}|p{0.15\textwidth}|} +% \hline +% \textbf{Suma punktów maksymalnych} & \textbf{Suma zdobytych punktów} & \textbf{Liczba realizowanych wymagań} & \textbf{Liczba zrealizowanych wymagań} & \textbf{Uzasadnienie} \\ +% \hline +% 5 & 5 & WS: 8 \\ WO: 5 \\ WP: 20 & WS: 1 (10.3) \\ WO: 2 (02.00, 05.00) \\ WP: 3 (01.03, 01.15, 01.20) & Zrealizowane wymagania: \\ Zad. 10.1: WS 10.3, WO 02.00, WO 05.00, WP 01.03, WP 01.15 \\ Zad. 10.2: WS 10.3, WO 02.00, WO 05.00, WP 01.03, WP 01.15, WP 01.20 \\ +% \hline +% \end{tabular} + +% ===================== Appendix ============================================== +\clearpage +\section*{Wszystkie wymagania edukacyjne} +\subsection*{Wymagania szczegółowe (Fizyka atomowa)} +\begin{itemize} + \item \hypertarget{ws-10.1}{\FmtSpec{WS 10.01}{\getRawCount{GlobalSpecCount10.1}}} – Analizuje na wybranych przykładach promieniowanie termiczne ciał i jego zależność od temperatury. + \item \hypertarget{ws-10.2}{\FmtSpec{WS 10.02}{\getRawCount{GlobalSpecCount10.2}}} – Opisuje dualizm korpuskularno-falowy światła; posługuje się pojęciem fotonu oraz oblicza jego energię. + \item \hypertarget{ws-10.3}{\FmtSpec{WS 10.03}{\getRawCount{GlobalSpecCount10.3}}} – Rozróżnia widma emisyjne i absorpcyjne gazów; interpretuje linie widmowe jako skutek przejść między poziomami energetycznymi w atomach z emisją lub absorpcją kwantu światła; rozróżnia stan podstawowy i stany wzbudzone atomu. + \item \hypertarget{ws-10.4}{\FmtSpec{WS 10.04}{\getRawCount{GlobalSpecCount10.4}}} – Analizuje seryjny układ linii widmowych na przykładzie widma atomu wodoru; oblicza różnice energii między poziomami energetycznymi w atomie wodoru. + \item \hypertarget{ws-10.5}{\FmtSpec{WS 10.05}{\getRawCount{GlobalSpecCount10.5}}} – Posługuje się pojęciem pędu fotonu; stosuje zasadę zachowania energii i zasadę zachowania pędu do opisu emisji i absorpcji przez swobodne atomy; opisuje odrzut atomu emitującego kwant światła. + \item \hypertarget{ws-10.6}{\FmtSpec{WS 10.06}{\getRawCount{GlobalSpecCount10.6}}} – Opisuje zjawiska jonizacji i fotoelektryczne jako wywołane tylko przez promieniowanie o częstotliwości większej od granicznej. + \item \hypertarget{ws-10.7}{\FmtSpec{WS 10.07}{\getRawCount{GlobalSpecCount10.7}}} – Opisuje zjawiska dyfrakcji oraz interferencji elektronów i innych cząstek; oblicza długość fali de Broglie’a poruszających się cząstek. + \item \hypertarget{ws-10.8}{\FmtSpec{WS 10.08}{\getRawCount{GlobalSpecCount10.8}}} – Doświadczalnie: obserwuje widma atomowe za pomocą siatki dyfrakcyjnej. +\end{itemize} + +\subsection*{Wymagania ogólne} +\begin{itemize} + \item \hypertarget{wo-1}{\FmtWO{WO 01.00}{\getRawCount{GlobalWOCount1}}} – Wykorzystanie pojęć i wielkości fizycznych do opisu zjawisk oraz wskazywanie ich przykładów w otaczającej rzeczywistości. + \item \hypertarget{wo-2}{\FmtWO{WO 02.00}{\getRawCount{GlobalWOCount2}}} – Rozwiązywanie problemów z wykorzystaniem praw i zależności fizycznych. + \item \hypertarget{wo-3}{\FmtWO{WO 03.00}{\getRawCount{GlobalWOCount3}}} – Planowanie i przeprowadzanie obserwacji oraz doświadczeń i wnioskowanie na podstawie ich wyników. + \item \hypertarget{wo-4}{\FmtWO{WO 04.00}{\getRawCount{GlobalWOCount4}}} – Posługiwanie się informacjami pochodzącymi z analizy materiałów źródłowych, w tym tekstów popularnonaukowych i źródeł internetowych, oraz ocenianie wiarygodności źródeł. + \item \hypertarget{wo-5}{\FmtWO{WO 05.00}{\getRawCount{GlobalWOCount5}}} – Budowanie modeli fizycznych i matematycznych do opisu zjawisk oraz ilustracji praw i zależności fizycznych. +\end{itemize} + +\subsection*{Wymagania przekrojowe (WP)} +\begin{itemize} + \item \hypertarget{wp-1.1}{\FmtWP{WP 01.01}{\getRawCount{GlobalWPCount1.1}}} – Przedstawia jednostki wielkości fizycznych, wyraża je poprzez jednostki podstawowe; przelicza wielokrotności i podwielokrotności. + \item \hypertarget{wp-1.2}{\FmtWP{WP 01.02}{\getRawCount{GlobalWPCount1.2}}} – Posługuje się materiałami pomocniczymi, w tym tablicami fizycznymi i chemicznymi oraz kartą wybranych wzorów i stałych fizykochemicznych. + \item \hypertarget{wp-1.3}{\FmtWP{WP 01.03}{\getRawCount{GlobalWPCount1.3}}} – Prowadzi obliczenia szacunkowe i poddaje analizie otrzymany wynik. + \item \hypertarget{wp-1.4}{\FmtWP{WP 01.04}{\getRawCount{GlobalWPCount1.4}}} – Przeprowadza obliczenia liczbowe, posługując się kalkulatorem. + \item \hypertarget{wp-1.5}{\FmtWP{WP 01.05}{\getRawCount{GlobalWPCount1.5}}} – Rozróżnia wielkości wektorowe i skalarne, wykonuje graficznie działania na wektorach (dodawanie, odejmowanie, mnożenie przez liczbę, rozkładanie na składowe). + \item \hypertarget{wp-1.6}{\FmtWP{WP 01.06}{\getRawCount{GlobalWPCount1.6}}} – Tworzy teksty, tabele, diagramy lub wykresy, rysunki schematyczne lub blokowe dla zilustrowania zjawisk bądź problemu; właściwie skaluje, oznacza i dobiera zakresy osi. + \item \hypertarget{wp-1.7}{\FmtWP{WP 01.07}{\getRawCount{GlobalWPCount1.7}}} – Wyodrębnia z tekstów, tabel, diagramów lub wykresów, rysunków schematycznych lub blokowych informacje kluczowe dla opisywanego zjawiska bądź problemu; przedstawia te informacje w różnych postaciach. + \item \hypertarget{wp-1.8}{\FmtWP{WP 01.08}{\getRawCount{GlobalWPCount1.8}}} – Rozpoznaje zależność rosnącą bądź malejącą na podstawie danych z tabeli lub na podstawie wykresu; rozpoznaje proporcjonalność prostą na podstawie wykresu. + \item \hypertarget{wp-1.9}{\FmtWP{WP 01.09}{\getRawCount{GlobalWPCount1.9}}} – Dopasowuje prostą do danych przedstawionych w postaci wykresu; interpretuje nachylenie tej prostej i punkty przecięcia z osiami. + \item \hypertarget{wp-1.10}{\FmtWP{WP 01.10}{\getRawCount{GlobalWPCount1.10}}} – Przeprowadza wybrane obserwacje, pomiary i doświadczenia na podstawie ich opisów; planuje i modyfikuje ich przebieg; formułuje hipotezę i prezentuje kroki niezbędne do jej weryfikacji. + \item \hypertarget{wp-1.11}{\FmtWP{WP 01.11}{\getRawCount{GlobalWPCount1.11}}} – Opisuje przebieg doświadczenia lub pokazu; wyróżnia kluczowe kroki i sposób postępowania oraz wskazuje rolę użytych przyrządów i uwzględnia ich rozdzielczość. + \item \hypertarget{wp-1.12}{\FmtWP{WP 01.12}{\getRawCount{GlobalWPCount1.12}}} – Przestrzega zasad bezpieczeństwa podczas wykonywania obserwacji, pomiarów i doświadczeń. + \item \hypertarget{wp-1.13}{\FmtWP{WP 01.13}{\getRawCount{GlobalWPCount1.13}}} – Wyznacza średnią z kilku pomiarów jako końcowy wynik pomiaru powtarzanego. + \item \hypertarget{wp-1.14}{\FmtWP{WP 01.14}{\getRawCount{GlobalWPCount1.14}}} – Posługuje się pojęciem niepewności pomiaru wielkości prostych; zapisuje wynik pomiaru wraz z jego jednostką oraz z uwzględnieniem informacji o niepewności; uwzględnia niepewności przy sporządzaniu wykresów. + \item \hypertarget{wp-1.15}{\FmtWP{WP 01.15}{\getRawCount{GlobalWPCount1.15}}} – Przeprowadza obliczenia i zapisuje wynik zaokrąglony do zadanej liczby cyfr znaczących. + \item \hypertarget{wp-1.17}{\FmtWP{WP 01.17}{\getRawCount{GlobalWPCount1.17}}} – Przedstawia własnymi słowami główne tezy tekstu popularnonaukowego z dziedziny fizyki lub astronomii. + \item \hypertarget{wp-1.18}{\FmtWP{WP 01.18}{\getRawCount{GlobalWPCount1.18}}} – Wyodrębnia zjawisko z kontekstu, nazywa je oraz wskazuje czynniki istotne i nieistotne dla jego przebiegu. + \item \hypertarget{wp-1.19}{\FmtWP{WP 01.19}{\getRawCount{GlobalWPCount1.19}}} – Tworzy modele fizyczne lub matematyczne wybranych zjawisk i opisuje ich założenia; ilustruje prawa i zależności fizyczne z wykorzystaniem tych założeń. + \item \hypertarget{wp-1.20}{\FmtWP{WP 01.20}{\getRawCount{GlobalWPCount1.20}}} – Posługuje się pojęciami pracy, mocy, energii kinetycznej; wykorzystuje równość między pracą siły wypadkowej i zmianą energii kinetycznej oraz zasadę zachowania energii mechanicznej do obliczeń. +\end{itemize} + +\end{document}