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Zero Order Reaction

If a is the i...

Question

If a is the initial concentration of reaction, then the half-life period of a reaction of nth order is:

A

α^{n}

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B

α^{n - 1}

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C

α^{1 - n}

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D

α^{n + 1}

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Solution

The correct option is C $α^{1 - n}$
Relation between half-life period of a reaction and initial concentration is as follows : $t^{1 / 2} \propto \frac{1}{a^{n - 1}}$
For First order reaction (Half life $\propto a^{0})$
For Second order reaction (Half life $\propto 1 / a)$
For Third order reaction (Half life $\propto 1 / a^{2})$

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1, α_{1}, α_{2}, α_{3}, . . ., α_{n - 1}

are the nth roots of unity, then the value of

1. α_{1} . α_{2} . α_{3} . . . α_{n - 1}

1, α_{1}, α_{2}, α_{3}, . . . . ., α_{n - 1}

are the nth roots of unity then show that

n = (1 - α_{1}) (1 - α_{2}) (1 - α_{3}) . . . . . (1 - α_{n - 1})

α_{0}, α_{1}, α_{2}, \dots, α_{n - 1}

n^{t h}

roots of unity, then

α_{k} = c o s (\frac{2 k π}{n}) + i s i n (\frac{2 k π}{n})

0 \leq k \leq n - 1

(x^{n} - 1) = (x - α_{0}) (x - α_{1}) \dots (x - α_{n - 1})

(1 + α_{0}) (1 + α_{1}) \dots (1 + α_{n - 1})

α_{1}

α_{2}

α_{n - 1}

are the nth roots of unity then

(1 - α_{1}) (1 - α_{2}) . . . (1 - α_{n - 1}) =

Q. If n is an odd positive integer and

I, α_{1}, α_{2}, . . . . α_{n - 1}

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roots of unity, then

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