Question

The diagram below shows:

•three of the pathways the alpha particles take.
•the number of alpha particles detected at positions A, B and C.
Determine the simplest ratio of the number of alpha particles detected at A to those detected at C. Use the diagram above.​

Answer 1

The simplest ratio of alpha particles detected at A to those detected at C is 13,000:3.

The given diagram illustrates the detection of alpha particles at three different positions: A, B, and C. The data indicates that 130,000 alpha particles are detected at A, 80,000 at B, and 30 at C. To determine the simplest ratio of the number of alpha particles detected at A to those detected at C, we compare the counts at A and C.

The ratio of A to C can be expressed as
`\( (130,000)/(30) \)`. To simplify this ratio, both terms are divided by their greatest common divisor, which is 10:

`\[ (130,000)/(30) = (13,000)/(3) \]`

Therefore, the simplest ratio of the number of alpha particles detected at A to those detected at C is 13,000:3.

In summary, for every 13,000 alpha particles detected at position A, only 3 alpha particles are detected at position C. This ratio captures the relative difference in the number of particles observed at these two locations based on the given data.