The value of one mincrocurie = .... disintegrations/second

Options

A. `3.7 xx 10^(5)`
B. `3.7 xx 10^(7)`
C. `3.7 xx 10^(4)`
D. `3.7 xx 10^(10)`

Explanation

To find the value of one microcurie in disintegrations per second, we can follow these steps:

### Step 1: Understand the definition of Curie
1. **Curie (Ci)** is a unit of radioactivity that is defined as the activity of a quantity of radioactive material in which 1 gram of radium-226 disintegrates at a rate of 3.7 × 10^10 disintegrations per second.

### Step 2: Convert Curie to Microcurie
2. **Microcurie (µCi)** is a subunit of Curie. It is defined as one-millionth of a Curie. Therefore, we can express this mathematically as:
\[ 1 \, \text{µCi} = 10^{-6} \, \text{Ci} \]

### Step 3: Calculate the disintegrations per second for Microcurie
3. To find the number of disintegrations per second for one microcurie, we multiply the number of disintegrations per second in one Curie by the conversion factor for microcuries:
\[ 1 \, \text{µCi} = 3.7 \times 10^{10} \, \text{disintegrations/second} \times 10^{-6} \]

### Step 4: Perform the multiplication
4. Now, we calculate:
\[ 1 \, \text{µCi} = 3.7 \times 10^{10} \times 10^{-6} = 3.7 \times 10^{4} \, \text{disintegrations/second} \]

### Final Answer
Thus, the value of one microcurie is:
\[ \text{1 µCi} = 3.7 \times 10^{4} \, \text{disintegrations/second} \]