Understand the effect of each decay

• In a $\beta^-$-decay, a neutron converts into a proton, so:

  • Atomic number increases by $1$
  • Mass number remains unchanged

• In an $\alpha$-decay, a helium nucleus $\left({}_2^4He\right)$ is emitted, so:

  • Atomic number decreases by $2$
  • Mass number decreases by $4$

Start with the given radionuclide

${}_{90}^{234}Th$

So initially:

• Atomic number $Z = 90$
• Mass number $A = 234$

After first $\beta^-$-decay

$Z = 90 + 1 = 91, \quad A = 234$

After second $\beta^-$-decay

$Z = 91 + 1 = 92, \quad A = 234$

After one $\alpha$-decay

$Z = 92 - 2 = 90, \quad A = 234 - 4 = 230$

Final radionuclide

• Atomic number $= 90$
• Mass number $= 230$

Match with options

This corresponds to:

Option B: $90$ and $230$

Comparison with stored correct answer

Stored correct answer: B

Our derived answer is also B, so they agree.