the half-life of tritium is 12.26 y

what would be the rate of decay of tritium atoms per second in 1.00 L of hydrogen gas at STP containing 0.15% tritium atoms ?

To calculate the rate of decay of tritium atoms per second in 1.00 L of hydrogen gas at STP containing 0.15% tritium atoms, you need to take the following steps:

Step 1: Calculate the number of tritium atoms in 1.00 L of hydrogen gas at STP.
Since the volume of the gas is given as 1.00 L, we can assume that the number of moles of hydrogen gas is 1. At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies 22.4 liters. So, in 1.00 L, there is (1/22.4) = 0.0446 moles of hydrogen gas.

Now, since 0.15% of the hydrogen gas is tritium atoms, we multiply the number of moles of hydrogen gas by 0.15% to find the number of moles of tritium atoms:
0.0446 moles * 0.15% = 0.0000669 moles

Step 2: Convert moles of tritium atoms to the number of tritium atoms.
To convert moles to atoms, we use Avogadro's number, which states that one mole of any substance contains 6.022 x 10^23 particles. Therefore, we multiply the number of moles by Avogadro's number to find the number of tritium atoms:
0.0000669 moles * (6.022 x 10^23 tritium atoms/mole) = 4.031278 x 10^19 tritium atoms

Step 3: Calculate the rate of decay of tritium atoms per second.
The rate of decay of tritium atoms per second can be determined using the concept of half-life and the given half-life of tritium, which is 12.26 years.

First, let's convert the half-life from years to seconds. There are 365 days in a year, 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute:
12.26 years * 365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 386,415,600 seconds

Now, we use the radioactive decay equation:
Rate of decay = (ln(2)) * (Number of atoms) / (Half-life)

Substituting the values:
Rate of decay = (ln(2)) * (4.031278 x 10^19 tritium atoms) / (386,415,600 seconds)

Using a calculator, we can solve this equation:
Rate of decay ≈ 1.091 x 10^10 tritium atoms/second

Therefore, the rate of decay of tritium atoms per second in 1.00 L of hydrogen gas at STP containing 0.15% tritium atoms is approximately 1.091 x 10^10 tritium atoms per second.