A 25.40 g sample of water containing tritium,(3/1)H , emits 1450 beta particles per second. Tritium is a weak beta emitter, with a half-life of 12.3 yr. What fraction of all the hydrogen in the water sample is tritium?
To find the fraction of all the hydrogen in the water sample that is tritium, we need to determine the number of tritium nuclei in the sample and divide it by the total number of hydrogen nuclei.
First, we need to calculate the number of tritium nuclei in the sample. Since we know the sample's mass, we can calculate the moles of tritium using its molar mass.
The molar mass of tritium (H-3) is 3.016 g/mol. Therefore, the number of moles of tritium can be found using the formula:
moles of tritium = mass of tritium / molar mass of tritium
By substituting the given values, we get:
moles of tritium = 25.40 g / 3.016 g/mol
Next, we need to calculate the total number of tritium nuclei. Since one mole of substance contains Avogadro's number (6.022 x 10^23) of particles, we multiply the number of moles of tritium by Avogadro's number:
total tritium nuclei = moles of tritium * Avogadro's number
Now, we need to determine the total number of hydrogen nuclei in the sample. We can find this by dividing the sample's mass by the molar mass of hydrogen (1.008 g/mol):
moles of hydrogen = mass of water / molar mass of hydrogen
By substituting the given values, we get:
moles of hydrogen = 25.40 g / 1.008 g/mol
Finally, we multiply the moles of hydrogen by Avogadro's number to get the total number of hydrogen nuclei:
total hydrogen nuclei = moles of hydrogen * Avogadro's number
Now, we can calculate the fraction of all the hydrogen in the water sample that is tritium by dividing the total number of tritium nuclei by the total number of hydrogen nuclei:
fraction of tritium = total tritium nuclei / total hydrogen nuclei
By substituting the values we calculated earlier, we can find the answer.
I would convert 12.3 years to seconds, then k = 0.693/t1/2.
rate = 1450 dps = kN
Solve for N = number of atoms.
Then determine the fraction that is of 25.40 g H2O H atoms. Remember H2O has two H atoms.