A 1.50- gas sample at 735 and 25.0 contains 5.00 radon-220 by volume. Radon-220 is an alpha-emitter with a half-life of 55.6 .
How many alpha particles are emitted by the gas sample in 4.00 minutes?
You don't have units for most of the numbers in the problem.
To determine the number of alpha particles emitted by the gas sample in 4.00 minutes, we need to consider the decay rate of radon-220 and the number of radon atoms present in the sample.
First, let's calculate the initial number of radon-220 atoms in the gas sample. We know that the gas sample contains 5.00 radon-220 by volume. Since radon-220 is an alpha emitter, each atom of radon-220 decays into an alpha particle. Therefore, the initial number of radon-220 atoms in the sample is also equal to the initial number of alpha particles.
To find the number of radon-220 atoms, we can use Avogadro's number (6.02 x 10^23 atoms/mole) and the molar mass of radon-220 (220 g/mole):
Number of radon-220 atoms = (5.00 moles) x (6.02 x 10^23 atoms/mole)
Next, we need to determine the decay rate of radon-220. The half-life of radon-220 is given as 55.6 seconds. The decay rate, which is the number of decays per unit time, is given by the equation:
Decay rate = (ln(2) / half-life) x Number of radon-220 atoms
Since the half-life is given in seconds, we need to convert 4.00 minutes to seconds:
4.00 minutes = (4.00 minutes) x (60 seconds/minute)
Now we can calculate the decay rate:
Decay rate = (ln(2) / 55.6 seconds) x Number of radon-220 atoms
Finally, to find the number of alpha particles emitted by the gas sample in 4.00 minutes, we multiply the decay rate by the time in seconds:
Number of alpha particles = Decay rate x 4.00 minutes
By substituting the values into the equations and performing the calculations, you can determine the number of alpha particles emitted by the gas sample in 4.00 minutes.