Question

The substance as a result of the chain of transformations loses one α_ and two β- particles and becomes U(234,92). Find the initial radioactive element ?

Answer 1

`color(white)(0)_(92)^(238)U`

Explanation:

`U(234.92)` I am assuming the comma should be a decimal point.

The mass number is 234, i.e. `color(white)(0)^(234)U`

We now look at how many neutrons and/or protons have been lost.

`alpha` particles contain 2 protons and 2 neutrons ( a helium nuclei )

`beta^+` and `beta^-` do not emit either neutrons or protons from the nucleus, they just convert one to the other and so do not change the mass number, but because a neutron changes to a proton in `beta^-` decay the atomic number increases by 1.

So the emission of two `beta^-` particles means.

`+ 2 \ \ \ \` protons.

Now we need to think about this. We lost 2 protons and two neutrons during `alpha` decay, so our mass went down by 4 and our atomic number went down by 2. during `beta^-` our atomic number went up by 2.

Altogether we lost 4 mass units.

We add these to the mass number.

`234+4=238`

This is our new mass number. The `color(white)(0)^(234)U` we started with was an isotope of uranium, this has an atomic number of 92. We still have an atomic number of 92.

Our new substance still has an atomic number of 92. This is sill uranium, but our mass number has increased to 238.

The isotope is therefore:

`color(white)(0)_(92)^(238)U`

Answer 2

Writing the reverse reaction we get

`"U"_234^92 +beta_0^-1+beta_0^-1+ "He"_4^2->"""X"_m^A`

Comparing Atomic numbers or charges we get
`92+(-1)+(-1)+2=A`
`=>A=92`

Comparing Atomic masses we get
`234+0+0+4=m`
`=>m=238`

We see that atomic number of parent is that of `"U"` and mass number is `=238`.

`:.` initial radioactive element is `"U"(238,92)`