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?

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780134112831

검증된 단계별 안내

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).

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.