I don't think so. The two are formed from breakdown of different unstable elements and they have very different water chemistry so even if they were formed in a fixed ratio the water chemistry would change their concentrations differently with time.

Thank you Dr. Henrik Rasmus Anderson for your answer. 

Best Regards

The ratio would be constant for a sealed container, equilibrium of concentrations after 30 days. A water sample taken from the environment or a water supply cannot be expected to be in equilibrium. The radium solubility will follow the water chemistry. Radium solubility of the water will determine the radium content. Radon will follow gas solubility of the water and the characteristics of matrix containing the water.

To get equilibrium between Radium and daughters (Rn-222, Pb-214, Bi-214...), you have to put the water in good sealed and tide container with enough wall thickness (to minimize the leak of Radon gas) for 25 days.

Water oftencarries radon in much higher concentrations than radium especially spring water. The concentration of radon could exceed 10Bq/l while radium is often at mBq/l levels. The radon of such concentrations is often called unsupported. The high radon concentrations reflect the way through underwater passed to i

It should not be the same for the water taken from normal/natural sources. For a detailed understanding about supported and unsupported issue, I recommend to read the following article: Radiation protection dosimetry 156 (2013), 475-480  

I agree with what was said: The radium-226 and radon-222 concentrations are in constant ratio (1:1) in radioactive equilibrium. But you cannot expect that your water samples, taken from environment, technologies or anywhere else, are in such equilibrium. The equilibrium between radium-226 and its daughter radon-222 can be reached in a gas-tight container. The time necessary to reach the radioactive equilibrium is about 30 days, which came from the radon-222 half life. Radium-226-radon-222 equilibrium is often used for radium-226 determination in water samples, where radium-226 is determined as radon-222 concentration in equilibrium.

It might be better to clarify the question, i.e. the ratio of 226Ra and 222Rn in natural water or using decay equilibrium between 226Ra and 22Rn for the Measurement of 226Ra. The most assumption for equlibrium of 226Ra and 222Rn in the above discussion is based on a long time (>25 days) waiting time, i.e. all original 222Rn in the water decays away, and the 222Rn in the Water is only produced from the radioactive decay of 226Ra.

Due to the different behaviors of Ra and Rn in the environment, the 226Ra/222Rn radioactive ratio in the natural water is not constant. Rn as gas can easily leaked and diffuse from the rocks/sediment to the water, while the disolution of Ra in the rock/sediment to the water is not so high, causing higher 222Rn concentration than that of 226Ra in the natural water. In addition, due to less solubility of gas Rn in water, it can diffuse from the water to air, if there is no extra source of Rn and Ra in teh water body, the diffusion of 222Rn produced from decay of 226Ra from the water to air, will cuase a lower 222Rn/226Ra ratio (

Excellent summary of the facts, Xiaolin.

When I fit the equations for the decay between the two, the intercept of the functions give me around 60 days. How do you guys find one month as a reference of secular equilibrium?

I attached the activity equations for mother and daughter nuclei.