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Standard VII

Chemistry

Sub-Atomic Particles

The half live...

Question

The half lives of radioactive elements $X$ and $Y$ are $3$ minute and $27$ minute respectively. If the activities of both are same, then the ratio of number of atoms of $X$ and $Y$ will be

1 : 9

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1 : 10

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1 : 1

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9 : 1

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Solution

The correct option is A $1 : 9$
As, $a c t i v i t y \propto n u m b e r o f a t o m s \times \frac{1}{h a l f - l i f e} \Rightarrow n u m b e r o f a t o m s \propto a c t i v i t y \times h a l f - l i f e$
So, the ratio of number of atoms of $X$ and $Y$ will be
$3 : 27 = 1 : 9$

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The half lives of radioactive elements X and Y are 3 minute and 27 minute respectively. If the activities of both are same, then the ratio of number of atoms of X and Y will be

The correct option is A 1:9As, activity∝number of atoms×1half−life⇒number of atoms∝activity×half−lifeSo, the ratio of number of atoms of X and Y will be3:27=1:9

The half lives of radioactive elements $X$ and $Y$ are $3$ minute and $27$ minute respectively. If the activities of both are same, then the ratio of number of atoms of $X$ and $Y$ will be

The correct option is A $1 : 9$
As, $a c t i v i t y \propto n u m b e r o f a t o m s \times \frac{1}{h a l f - l i f e} \Rightarrow n u m b e r o f a t o m s \propto a c t i v i t y \times h a l f - l i f e$
So, the ratio of number of atoms of $X$ and $Y$ will be
$3 : 27 = 1 : 9$