Five radioactive samples are measured over three days using a Geiger-Muller tube to provide a count rate. Which of the samples has a half-life of two days?
A radioactive sample can undergo radioactive decay. Radioactive decay is the spontaneous emission of radiation by an unstable nucleus. The Geiger-Muller tube is used for detecting radiation, and it is attached to a Geiger counter. When radiation enters the tube, an electrical pulse is sent to the counter. The counter displays the count rate. The count rate is the number of radiation detection events, such as electrical pulses per second or per minute.
The half-life is the amount of time required for one-half of the radioactive nuclei in a sample to decay. As the radioactive nuclei decay, then less radiation will be released. When radiation collides with an atom, it can cause the atom to lose an electron. So we can call it ionizing radiation.
If there’s less ionizing radiation released, there will be fewer radiation detection events. Thus, the count rate will decrease. Therefore, the count rate directly correlates to the amount of radioactive material remaining. This means that the half-life can be described as the amount of time required for one-half of the radioactive nuclei in a sample to decay or the amount of time required for the count rate to decrease to half of its original value.
We want to find out which of the samples has a half-life of two days. So we need to see which source’s count rate halves after two days. The day-two column doesn’t represent the count rate after two days but rather the count rate after one day of monitoring. Therefore, the day-three column contains the count rate after two days. We need to compare the count rate between the day one and the day-three column. We have already established that as the radioactive nuclear decay, the count rate will decrease.
We need to find out how much smaller the values in the day-three column are than in the day-one column. So for each of the sources, we need to divide its value in the day-three column by its value in the day-one column. For source 𝐴, this will be 300 divided by 1200. Therefore, the count rate after two days is a quarter of the original count rate. But we want to find the half-life, so the count rate needs to be half of its original value, not a quarter.
For source 𝐵, we need to calculate 85 divided by 100. This gives us 17 over 20 or 0.85. For source 𝐶, we need to calculate 300 divided by 600. This gives us the value one-half, so after two days the count rate has decreased to half of its original value. This means that sample 𝐶 has a half life of two days and is the answer to this question. But just to make sure, let’s check the values for source 𝐷 and 𝐸. Neither source 𝐷 nor 𝐸 gives a value of one-half. So we know that the answer to the question “which of the samples has a half-life of two days?” is source 𝐶.