Radon-226 Decay: Half-Life of Radium-226

[vanceEE]

"Radium-226 has a half-life of 1,620 years, which means that half of a given sample of radium-226 will decay into lead by the end of 1,620 years. In the next 1,620 years, half of the remaining sample will decay into lead, leaving one-fourth of the original amount of radium-226."(1)

Wouldn't half of the Radium-226 decay into Radon-222 instead of Lead? I am new to this but my previous knowledge of decay from Physics tells me that Radium would would first decay to Radon by the end of 1,620 years which can be described by the equation below:
$\stackrel{226}{86}Ra→ \stackrel{222}{84}Rn + \stackrel{4}{2}He$

Is (1) a misprint or am I missing the half-life concept?

 

[snorkack]

The main branch daughters of radium are:
radium emanation, half-life 3,8 days
radium A, 3,1 minutes
radium B (lead 214) 27 minutes
radium C 20 minutes
radium C' 165 microseconds
radium D (lead 210) 22,2 years
radium E 5 days
radium F 138,4 days
The final product, stable radium G, is lead 206.
So all non-lead daughters of radium have a combined half-life of under 148 days. Over the 1600 year half-life of radium, almost all that has decayed into radium emanation has gone on to lead.

 

[Borek]

I think it should be more like

^{226}_{\phantom{0}88}Ra \rightarrow {}^{222}_{\phantom{0}86}Ba + ^{4}_{2}He

Edit: this is wrong, idiotic mistake. See below.

What they mean is most likely that there is a long decay chain which ends with Pb. If most steps are faster, that's effectively as if the Ra was decaying into Pb with a given half life.

 

[DrDu]

I think it should be more like

$$^{226}_{\phantom{0}88}Ra \rightarrow {}^{222}_{\phantom{0}86}Ba + ^{4}_{2}He$$

Are you really sure about Barium?

 

[Borek]

Sigh, I copy pasted nice LaTeX from another post - and I corrected atomic masses, but got distracted and left Ba from the original code

$$^{226}_{\phantom{0}88}Ra \rightarrow {}^{222}_{\phantom{0}86}Rn + ^{4}_{2}He$$

 

[DrDu]

:-)
How about
$$\mathrm{^{226}_{\phantom{0}88}Ra \rightarrow {}^{222}_{\phantom{0}86}Rn + ^{4}_{2}He}$$?