JEE MAIN - Chemistry (2004 - No. 42)
Consider the following nuclear reactions
$${}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He$$
$${}_Y^XN \to {}_B^AL + 2{\beta ^ + }$$
The number of neutrons in the element L is
$${}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He$$
$${}_Y^XN \to {}_B^AL + 2{\beta ^ + }$$
The number of neutrons in the element L is
140
144
142
146
Explanation
We know that, $\alpha$ - decay formula is -
$$ { }_Z^A X \stackrel{-\alpha}{\rightarrow}{ }_{Z-2}^{A-4} Y $$
And the formula for $\beta$ is -
$$ { }_Z^A X \stackrel{-\beta}{\rightarrow}{ }_{Z-1}^A Y $$
Now for the given above question we see that, -
$$ \begin{aligned} &{ }_{92}^{238} M \stackrel{-2 \alpha}{\rightarrow}{ }_{92-4}^{238-8} N \\\\ &{ }_Y^X X \stackrel{-2 \beta^{+}}{\rightarrow}{ }_{86}^{230} L \end{aligned} $$
Therefore we can now calculate the number of neutrons in $L$, -
$$ L=230-86 $$
$$ L=144 $$
So, as we can see the no. of neutrons present in $\mathrm{L}$ is 144 .
$$ { }_Z^A X \stackrel{-\alpha}{\rightarrow}{ }_{Z-2}^{A-4} Y $$
And the formula for $\beta$ is -
$$ { }_Z^A X \stackrel{-\beta}{\rightarrow}{ }_{Z-1}^A Y $$
Now for the given above question we see that, -
$$ \begin{aligned} &{ }_{92}^{238} M \stackrel{-2 \alpha}{\rightarrow}{ }_{92-4}^{238-8} N \\\\ &{ }_Y^X X \stackrel{-2 \beta^{+}}{\rightarrow}{ }_{86}^{230} L \end{aligned} $$
Therefore we can now calculate the number of neutrons in $L$, -
$$ L=230-86 $$
$$ L=144 $$
So, as we can see the no. of neutrons present in $\mathrm{L}$ is 144 .
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