Question #575fe

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Question #575fe

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Answer 1 · 2016-06-23T20:22:48

$_{a 47}^{113} Ag \to_{a 48}^{113} Cd +_{- 1}^{a a 0} β + {¯ ν}_{e}$ $""_ (color(white)(a)47)^113"Ag" -> ""_ (color(white)(a)48)^113"Cd" + ""_ (-1)^(color(white)(aa)0)beta + bar(nu)_"e"$

Explanation:

Your strategy here will be to use the fact that in a nuclear reaction, mass and charge are conserved.

In your case, the nuclear reaction involves the decay of silver-113 to cadmium-113

$_{a 47}^{113} Ag \to_{a 48}^{113} Cd +_{x}^{y} ?$ $""_ (color(white)(a)47)^113"Ag" -> ""_ (color(white)(a)48)^113"Cd" + ""_color(red)(x)^color(blue)(y)?$

Your goal now is to find the values of $x$ $color(red)(x)$ and $y$ $color(blue)(y)$ . You can write

$113 = 113 + y \to$ $113 = 113 + color(blue)(y) ->$ conservation of mass

$a 47 = a 48 + x \to$ $color(white)(a)47 = color(white)(a)48 + color(red)(x) ->$ conservation of charge

This gets you

$113 = 113 + y \Rightarrow y = 0$ $113 = 113 + color(blue)(y) implies color(blue)(y) = 0$

and

$47 = 48 + x \Rightarrow x = 47 - 48 = - 1$ $47 = 48 + color(red)(x) implies color(red)(x) = 47 - 48 = -1$

Therefore, your unknown particle has a mass number of $0$ $0$ and a charge of $1 -$ $1-$ . At this point, you should recognize that your unknown particle is a high-speed electron, also called beta particle, $_{- 1}^{a a 0} β$ $""_(-1)^(color(white)(aa)0)beta$ .

The nuclear equation given to you describes the beta minus decay of silver-113.

$_{a 47}^{113} Ag \to_{a 48}^{113} Cd +_{- 1}^{a a 0} β$ $""_ (color(white)(a)47)^113"Ag" -> ""_ (color(white)(a)48)^113"Cd" + ""_(-1)^(color(white)(aa)0)beta$

It's worth mentioning that beta minus decay also produces an electron antineutrino, ${¯ ν}_{e}$ $bar(nu)_"e"$ , so the complete nuclear equation would look like this

$color(green)(|bar(ul(color(white)(a/a)color(black)(""_ (color(white)(a)47)^113"Ag" -> ""_ (color(white)(a)48)^113"Cd" + ""_ (-1)^(color(white)(aa)0)beta + bar(nu)_"e")color(white)(a/a)|)))$

As you can see, in beta minus decay, a neutron is converted into a proton and an electron and an antineutrino are emitted from the nucleus.

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