1) SPM 2013 Physics Paper 1 has an interesting question on half-life calculation.

(Shouldn't there be another choice, say:

25% have decayed means 75% have not decayed. And that means, its half-life > 15 minutes. So was the half-life A, B or none of the 4 given choices? Do you not agree that the half life should be calculated as follows:

=

Based on

But

So,

Isn't this question both interesting and bewildering?! :)

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**Q 48 reads:**

**"25% of Gallium-65 atoms have decayed after 15 minutes. What is the half-life of Gallium-65?****A**30.0 minutes**B**23.4 minutes**C**15.0 minutes**D**7.5 minutes(Shouldn't there be another choice, say:

**E**36+ minutes?)**:**__My Comments (based on info given in the Q48)____Half-life of Gallium-65 based on info given in the Q48:__25% have decayed means 75% have not decayed. And that means, its half-life > 15 minutes. So was the half-life A, B or none of the 4 given choices? Do you not agree that the half life should be calculated as follows:

__The 1/4-life Method:__

__At the end of 15 minutes (1st 1/4-life)__:

a) amount decayed = 25% =

**¼**of original amount
b) amount undecayed = 75% = ¾ of original amount

__At the end of 30__:

^{ }minutes (2nd 1/4-life)
a) amount decayed =

**¼**x ¾ of original amount = 3/16 of original amount
b) total amount decayed = (¼ + 3/16) of original amount = 7/16 of the original amount

c) total amount undecayed = (1 – 7/16) of original amount = 9/16 of the original amount

__To decay to ½ (or 8/16) of original amount__:

a) A further 1/16 is to be decayed

b) 1/16 = [(

**1/4**) x (9/16)] x (4/9)
c) Time needed = [15 minutes] x (4/9) = 6.67 minutes

__= (15 + 15 + 6.67) minutes__

**Therefore, half-life**__36.67minutes__**Answer**

**A**(30 minutes) cannot be the acceptable answer because in 30 minutes only 7/16 and not 1/2 (or 8/16) of the radioactive substance has decayed. Conceptually,**A**is a wrong answer. Q48, to me, has no acceptable answers. This is also confirmed by logarithm method of calculating half-life as follows:

__Logarithm Method to Calculate Number of Half-Lives:__
Let: n = number of
half-lives

A

_{o}= Original amount of radioactive substance (or original level of radioactivity)
A

_{c}= Current amount of radioactive substance (or current level of radioactivity)
Then, (1/2)

^{n}x A_{o}= A_{c}
(1/2)

^{n}= A_{c}/A_{o}
(1/2)

^{n}= 0.75A_{o}/A_{o}= 0.75
log
both sides: log
(1/2)

^{n}= log (0.75)
Hence,

__n = log (____0.75) ÷ log (1/2) = 0.415037499 half-life__

__To Calculate the Half-Life, T___{1/2}
Let T

_{1/2}= Half-life time
T

_{o}= Time as at original amount of radioactive substance
(or original
level of radioactivity)

T

_{c}= Time as at current amount of radioactive substance
(or current
level of radioactivity)

n = number
of half-lives

Then,

__T___{1/2}= (T_{c}- T_{o}) ÷ n = 15 minutes ÷ n = 15 min ÷ [__log (0.75) ÷ log (1/2)]__

__T___{1/2}= 36.14131259

__T___{1/2}= 36.1 minutesBased on

**facts given in Q48**,**logarithm method**shows a half-life 36.1 minutes.But

**online searches**(please click here or here) show that isotopes Gallium-65 actually have a half-life of 15.2 minutesSo,

**which is the examiners' preferred answer and why?**Isn't this question both interesting and bewildering?! :)

In conclusion: Overall, except for Q48, Paper 1 is still a good paper - of respectable standard! :)

(10.4.2014: The examiners should have replaced the words "Gallium-65" in Q 48 with the words "isotopes-X". Otherwise, it's like a biology question on man that talks about the man having ovaries, uterus, etc. that makes the candidates wonder whether it is a question about man or something else. The more well-read the students, the more disadvantaged he/she would be - that is ridiculous!)

(10.4.2014: The examiners should have replaced the words "Gallium-65" in Q 48 with the words "isotopes-X". Otherwise, it's like a biology question on man that talks about the man having ovaries, uterus, etc. that makes the candidates wonder whether it is a question about man or something else. The more well-read the students, the more disadvantaged he/she would be - that is ridiculous!)

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