What is the isotope remaining when uranium-235 decays in the following steps: #α, α, γ, β#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Ernest Z.
Apr 28, 2017

The isotope remaining will be #""_89^227"Ac"#.

Explanation:

First α decay

#""_92^235"U" → color(white)(l)_90^231"Th" +color(white)(l) _2^4"He"#

Second α decay

#""_90^231"Th" →color(white)(l) _88^227"Ra"^"*" + color(white)(l)_2^4"He"#

I presume that the radium isotope is in a metastable state, because it emits a γ ray in the next step

Gamma decay

#""_88^227"Ra"^"*" → color(white)(l)_88^227"Ra"+ γ#

β Decay

#""_88^227"Ra" → color(white)(l)_89^227"Ac" +color(white)(l) _text(-1)^0"e"#

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