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Terminology and concepts related to Physics, Chemistry & Mathematics.



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ALCOHOLS

Alcohol Oxidation with Potassium Dichromate

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Potassium dichromate oxidises 1o and 2o alcohols and gets reduced to green Cr3+ ion.

In case of 3o alcohols the bright orange colour of dichromate ion remains as it is indicating no reaction.

The colour change can be used to indicate a reaction. If the orange colour changes to green or blue green a reaction has occurred.

fig.

Hemiacetal

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It is the product of nucleophilic addition of an aldehyde or ketone to an alcohol. 1 molecule of alcohol adds to 1 molecule of aldehyde or ketone to yield hemiacetal.

Formula: RCR'(OR")(OH). OR" has been supplied by the alcohol whereas R and R' originally belong to the aldehyde or ketone. If it is an aldehyde, then one of the two i.e. R or R' must be H.

PS: Hemi means half. Hemiketal name is no longer in use by IUPAC, it was used in the past to distinguish between aldehydes & ketones.

ATOMIC STRUCTURE

Heisenberg Uncertainty Principle

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It would be impossible to make accurate measurements of certain pairs of properties, since any technique used for measuring one of them will disturb the system and will cause the measurement of the other one to be imprecise. For instance the method used to measure the position of the particle will result in an uncertainty in the precision of the measurement of the momentum of the particle.

ELECTROCHEMISTRY

Faraday's Laws of Electrolysis

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1st Law: The weight of a given element liberated at an electrode is proportional to the quantity of electricity passed through the solution.

2nd Law: The weights of different elements liberated by same quantity of electricity are proportional to the equivalent weights of the elements.

3rd Law: It is known experimentally that 1F (96500 C) always liberates 1g equivalent of a substance.

FUNCTIONS

Even & Odd Function

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Even Function: If a function f is such that f(-x)=f(x), then the function f is called even function.

Odd Function: If a function f is such that f(-x)=-f(x), then the function f is called odd function.

Period of constant function

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Constant function is a special case of periodic function. Period of constant function can be any positive real number except zero.

INTEGRATION

Cauchy-Bunyakovsky Inequality

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\left|{\int\limits_a^b{f(x)g(x)dx}}\right|\le\sqrt{\int\limits_a^b {f^2 (x)dx}}\sqrt{\int\limits_a^b{g^2(x)dx}}

Leibnitz's Rule

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{d \over {dx}}\left[ {\int_{g(x)}^{h(x)} {f(x,t)dt} } \right] = \int_{g(x)}^{h(x)} {{\partial \over {\partial x}}f(x,t)dt + h'(x)f\{ x,h(x)\} - g'(x)f\{ x,g(x)\} }

A simplified situation arises when f depends only on t, making the partial derivative term zero.

{d \over {dx}}\left[ {\int_{g(x)}^{h(x)} {f(t)dt} } \right] = \int_{g(x)}^{h(x)} {{\partial \over {\partial x}}f(t)dt + h'(x)f\{ x,h(x)\} - g'(x)f\{ x,g(x)\} }

\Rightarrow {d \over {dx}}\left[ {\int_{g(x)}^{h(x)} {f(t)dt} } \right] = 0 + h'(x)f\{ x,h(x)\} - g'(x)f\{ x,g(x)\}

\Rightarrow {d \over {dx}}\left[ {\int_{g(x)}^{h(x)} {f(t)dt} } \right] = h'(x)f\{ x,h(x)\} - g'(x)f\{ x,g(x)\}

Walli's Formula

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\int\limits_0^{{\pi\over2}}{\sin^m x\cos ^n xdx={{[(m-1)(m-3)..................2or1][(n-1)(n-3)...............2or1]}\over {[(m+n)(m+n-2).................2or1]}}}

Multiply the above result by \frac{\pi}{2} only when both n and m are even (treat o as even).

KINEMATICS

Inclined Plane Projectile Range

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