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 determine the rate of decay of tritium atoms per second in 1.00 L of hydrogen gas at STP containing 0.15% tritium atoms, we need to use the following steps:
Step 1: Convert the given concentration of tritium atoms to a decimal.
0.15% = 0.15/100 = 0.0015
Step 2: Calculate the number of tritium atoms in 1.00 L of hydrogen gas using Avogadro's number.
Avogadro's number (Na) = 6.022 × 10^23 atoms/mol
Number of tritium atoms in 1.00 L = 0.0015 × Na
Step 3: Calculate the rate of decay per second using the half-life of tritium.
Half-life of tritium (t1/2) = 12.26 years = 12.26 × 365 × 24 × 60 × 60 seconds
Rate of decay per second = (Number of tritium atoms in 1.00 L) / (t1/2)
Now let's calculate the rate of decay of tritium atoms per second in 1.00 L of hydrogen gas at STP containing 0.15% tritium atoms.
Please note that this calculation assumes that all tritium atoms decay at the same rate, which may not be exactly accurate due to random nature of decay, but provides a good approximation.
To calculate the rate of decay of tritium atoms per second in 1.00 L of hydrogen gas, we need to consider a few steps:
Step 1: Determine the number of tritium atoms in 1.00 L of hydrogen gas at STP.
We can use Avogadro's number (6.022 x 10^23 atoms per mole) to convert the concentration of tritium atoms (0.15%) to moles.
- Concentration of tritium atoms = 0.15% = 0.15/100 = 0.0015
- Moles of tritium atoms = concentration x volume (in liters)
- Moles of tritium atoms = 0.0015 x 1.00 = 0.0015
Step 2: Calculate the number of moles of tritium that decay in 1.00 L of hydrogen gas over a time of 1 second.
The decay follows a first-order reaction, so we can use the equation:
- Nt = N0 x (1/2)^(t/t1/2)
where Nt is the final number of atoms, N0 is the initial number of atoms, t is the time elapsed, t1/2 is the half-life of tritium.
- Nt = N0 x (1/2)^(1/1.00)
- Nt = N0 x (1/2)
So, half of the tritium atoms will decay in 1.00 second.
Step 3: Calculate the rate of decay of tritium atoms in 1.00 L of hydrogen gas per second.
We know that 0.0015 moles of tritium atoms will decay in 1 second, and there are 6.022 x 10^23 atoms per mole.
- Number of tritium atoms decaying per second = 0.0015 moles x 6.022 x 10^23 atoms/mole
- Number of tritium atoms decaying per second = 9.033 x 10^20 atoms/second
So, the rate of decay of tritium atoms in 1.00 L of hydrogen gas containing 0.15% tritium atoms at STP is approximately 9.033 x 10^20 atoms per second.