A 1.50-L gas sample at 745 mm Hg and 25.0 °C contains 3.55% radon-220 by volume. Radon-220 is an alpha emitter with a half-life of 55.6 s. How many alpha particles are emitted by the gas sample in 5.00 minutes?

Verified step by step guidance

Convert the initial conditions of the gas sample to standard units: pressure in atm and temperature in Kelvin.

Use the ideal gas law, PV = nRT, to calculate the total number of moles of gas in the sample.

Determine the volume percentage of radon-220 in the gas sample and calculate the moles of radon-220 using the percentage given.

Calculate the initial number of radon-220 atoms using Avogadro's number.

Use the half-life of radon-220 to determine the number of alpha particles emitted in 5.00 minutes by applying the decay formula: N(t) = N_0 * (1/2)^(t/half-life).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the number of moles of radon-220 in the gas sample, which is necessary for determining the amount of alpha particles emitted.

Radioactive Decay and Half-Life

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. The half-life is the time required for half of the radioactive atoms in a sample to decay. Understanding half-life is crucial for calculating how many radon-220 atoms remain after a certain time, which directly affects the number of alpha particles emitted.

Volume Percent Concentration

Volume percent concentration expresses the amount of a substance in a mixture as a percentage of the total volume. In this case, knowing that radon-220 constitutes 3.55% of the gas sample allows for the calculation of the actual volume of radon-220 present, which is necessary for determining the total number of alpha particles emitted during decay.