From 0101cfe0300704ddcf5cbcac347465d482eae7ff Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Tue, 28 Aug 2018 11:26:45 +1000 Subject: [PATCH] antidiff applications & photoelectric graphics --- physics/graphics/energy-levels.png | Bin 0 -> 123528 bytes physics/graphics/photoelectric-effect.png | Bin 0 -> 333884 bytes physics/graphics/standing-wave-electrons.png | Bin 0 -> 140277 bytes physics/graphics/synchrotron.png | Bin 0 -> 380671 bytes physics/light-matter.md | 10 ++++++++++ spec/calculus.md | 12 +++++++++++- 6 files changed, 21 insertions(+), 1 deletion(-) create mode 100644 physics/graphics/energy-levels.png create mode 100644 physics/graphics/photoelectric-effect.png create mode 100644 physics/graphics/standing-wave-electrons.png create mode 100644 physics/graphics/synchrotron.png diff --git a/physics/graphics/energy-levels.png b/physics/graphics/energy-levels.png new file mode 100644 index 0000000000000000000000000000000000000000..1b1d59a93f54229ebce64a984b2ed5ce6ac52050 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if $2\pi r \ne n{h \over mv}$, interference occurs when pattern is looped and standing wave cannot be established +![](graphics/standing-wave-electrons.png) + ### Photon momentum $$\rho = {hf \over c} = {h \over \lambda}$$ @@ -104,6 +108,9 @@ $$\rho = {hf \over c} = {h \over \lambda}$$ - Black lines in spectrum show light not reflected ### Emission + +![](graphics/energy-levels.png) + - Coloured lines show light being ejected from e- shells - Energy change between ground / excited state: $\Delta E = hf = {hc \over \lambda}$ - Bohr's model describes discrete energy levels @@ -112,6 +119,9 @@ $$\rho = {hf \over c} = {h \over \lambda}$$ - EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) ## Light sources + +![](graphics/synchrotron.png) + - **incandescent:** <10% efficient, broad spectrum - **LED:** semiconducting doped-Si diodes - - most electrons in *valence band* (energy level) diff --git a/spec/calculus.md b/spec/calculus.md index 08cfe8f..f68b829 100644 --- a/spec/calculus.md +++ b/spec/calculus.md @@ -194,7 +194,7 @@ $\int k f(x) dx = k \int f(x) dx$ | ------------------------------- | ---------------------------- | | $k$ (constant) | $kx + c$ | | $x^n$ | ${1 \over {n+1}}x^{n+1} + c$ | -| $a \cdot {1 \over x}$ | $a \cdot \log_e x + c$ | +| $a x^{-n}$ | $a \cdot \log_e x + c$ | | $e^{kx}$ | ${1 \over k} e^{kx} + c$ | | $e^k$ | $e^kx + c$ | | $\sin kx$ | $-{1 \over k} \cos (kx) + c$ | @@ -202,5 +202,15 @@ $\int k f(x) dx = k \int f(x) dx$ | ${f^\prime (x)} \over {f(x)}$ | $\log_e f(x) + c$ | | $g^\prime(x)\cdot f^\prime(g(x)$ | $f(g(x))$ (chain rule)| | $f(x) \cdot g(x)$ | $\int [f^\prime(x) \cdot g(x)] dx + \int [g^\prime(x) f(x)] dx$ | +| ${1 \over {ax+b}}$ | ${1 \over a} \log_e (ax+b) + c$ | +| $(ax+b)^n$ | ${1 \over {a(n+1)}}(ax+b)^{n-1} + c$ | + +## Applications of antidifferentiation + +- $x$-intercepts of $y=f(x)$ identify $x$-coordinates of stationary points on $y=F(x)$ +- the nature of any stationary point of $y=F(x)$ is determined by the way the sign of the graph of $y=f(x)$ changes about its $x$-intercepts +- if $f(x)$ is a polynomial of degree $n$, then $F(x)$ has degree $n+1$ + +To find stationary points of a function, substitute $x$ value of given point into derivative. Solve for ${dy \over dx}=0$. Integrate to find original function. -- 2.52.0

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