Hi Farhaini,

### SPM Physics Radioactivity Question

- A rate meter of a G-M tube recorded a background reading 40 counts per minute. When a radioactive element is put in front of the G-M tube, the rate meter reads 160 counts per minute. After 6 hours, the rate meter become 55 counts per minute.

Meter kadar pada satu tiub G-M mencatatkan sinaran latar belakang 40 bilangan per minit. Apabila satu bahan radioaktif diletakkan di hadapan tiub G-M, meter kadar mencatatkan 160 bilangan per minit. Selepas 6 jam, bacaan meter kadar menjadi 55 bilangan per minit.Determine the half life of the radioactive element.

Tentukan separuh hayat bagi bahan radioaktif itu.A. 2 hours.

2 jam.

B. 4 hours.

4 jam.

C. 6 hours.

6 jam.

D. 12 hours.

12 jam.

### SPM Physics Radioactivity Solution

We can begin by looking at the definition:

Real reading= Measured reading - Background reading

Half life= time taken for the radioactivity of an isotope to fall to half its initial value

**Half life formula:**

**Applying the formula above:**

Initial real reading = 160 - 40 = 120

Final real reading (after 6 hrs) = 55 - 40 = 15

**Plugging in the values into the half life formula:**

t = 6 hrs

N = Final reading = 15

No = Initial reading = 120

15 = 120 * (1/2)^(6 / half life)

15/120 = (1/2)^(6 / half life)

**Adding log on both side to simplify the equation:**

log(15/120) = log[(1/2)^(6 / half life)]

**Logarithm rule: bring power down**

log(15/120) = (6 / half life) * log(1/2)

**Rearrange:**

log(15/120) / log(1/2) = 6 / half life

3 = 6/half life

**Final Answer:**

half life = 6 / 3 = 2 hours

I understand now Thank you very much!