The answer isn’t really taking the value for the background radiation from the gamma radiation. Here’s some more detail on what the answer is saying:
When the source is 10cm from the detector, no alpha radiation is received at the detector, so the counter receives background radiation, plus beta and gamma radiation, and this totals 100 counts/s.
When the aluminum plate is put in front of the detector, it cuts off the beta radiation, but not the background or gamma radiation, and this totals 50 counts/s. Therefore the beta radiation must have been 50 counts/s.
When the source is taken away completely the detector only gets background radiation. Therefore the gamma radiation must have been 40 counts/s.
Going back to the starting state, when the counter was receiving background radiation, plus beta and gamma radiation, if the source is moved much closer the counter will also receive alpha radiation, so when the rate goes up from 100 to 400 counts/s, this extra 300 counts/s must have been the alpha radiation.
Hi,
Correct me if I am wrong but surely since the aluminium plate it held in front of the detector, it should block the background radiation as well as the beta? This meant I got the ratios of the beta and gamma the other way around. I agree with your result if the aluminium is held in front of the source however given the 10cm gap and it says in front of the detector, I cannot understand why it is this way around.
You won’t generally block most background radiation by putting an aluminum sheet in front of a detector no matter how close it is. Things you won’t block include: cosmic rays, environmental gamma radiation, gaseous radon, micro-particles, …
By the way, remember that this sort of question won’t come up in the 2016 test because the syllabus has changed.
But shouldn’t the intensity of the gamma radiation become 100 times stronger if you tenth the distance that the source is to the detector? Or am I missing something here?
You mean “doesn’t gamma radiation obey an inverse square law?”. Yes it would if it were a point source of radiation, but the question says the source “emits a parallel beam”, so this does not change in intensity with distance, so in this case, no.
Oxford PAT 
Hi, thank you so much for this site!
I was just wondering why the value for the background radiation is taken away from the gamma radiation and not the beta radiation?
Thank you 🙂
The answer isn’t really taking the value for the background radiation from the gamma radiation. Here’s some more detail on what the answer is saying:
When the source is 10cm from the detector, no alpha radiation is received at the detector, so the counter receives background radiation, plus beta and gamma radiation, and this totals 100 counts/s.
When the aluminum plate is put in front of the detector, it cuts off the beta radiation, but not the background or gamma radiation, and this totals 50 counts/s. Therefore the beta radiation must have been 50 counts/s.
When the source is taken away completely the detector only gets background radiation. Therefore the gamma radiation must have been 40 counts/s.
Going back to the starting state, when the counter was receiving background radiation, plus beta and gamma radiation, if the source is moved much closer the counter will also receive alpha radiation, so when the rate goes up from 100 to 400 counts/s, this extra 300 counts/s must have been the alpha radiation.
That makes a lot more sense, thank you so much!
Hi,
Correct me if I am wrong but surely since the aluminium plate it held in front of the detector, it should block the background radiation as well as the beta? This meant I got the ratios of the beta and gamma the other way around. I agree with your result if the aluminium is held in front of the source however given the 10cm gap and it says in front of the detector, I cannot understand why it is this way around.
You won’t generally block most background radiation by putting an aluminum sheet in front of a detector no matter how close it is. Things you won’t block include: cosmic rays, environmental gamma radiation, gaseous radon, micro-particles, …
By the way, remember that this sort of question won’t come up in the 2016 test because the syllabus has changed.
But shouldn’t the intensity of the gamma radiation become 100 times stronger if you tenth the distance that the source is to the detector? Or am I missing something here?
You mean “doesn’t gamma radiation obey an inverse square law?”. Yes it would if it were a point source of radiation, but the question says the source “emits a parallel beam”, so this does not change in intensity with distance, so in this case, no.