Which of the following statements about nuclear transformations are correct?

AOne $α$ emission followed by two $β^{-}$ emissions gives an isotope of the parent nuclide.
BOne $α$ emission followed by one $β^{-}$ emission gives an isobar of the parent nuclide.
CPositron emission and K-electron capture both lower the atomic number by one without changing the mass number.
DEmission of a $γ$ photon lowers the mass number by one.

Answer: A, C

α

Δ Z = - 2

Δ A = - 4

;

β^{-}

Δ Z = + 1

. So

α + 2 β^{-}

restores

Z

, giving an isotope (A true).

α + β^{-}

changes

A

by 4, so it is not an isobar (B false).

β^{+}

and K-capture each give

Δ Z = - 1

Δ A = 0

(C true).

γ

emission changes neither

Z

nor

A

(D false).