If P is X-ray unit and Q is micron, then `P/Q`=

Options

A. `10^(7)`
B. `10^(-7)`
C. `10^5`
D. `10^(-3)`

Answer

To solve the problem of finding the ratio \( \frac{P}{Q} \) where \( P \) is the unit of X-ray wavelength and \( Q \) is in microns, we can follow these steps:

### Step 1: Identify the units
- The unit of X-ray wavelength \( P \) is typically in nanometers (nm).
- The unit \( Q \) is given in microns (µm).

### Step 2: Convert the units to meters
- We know that:
- \( 1 \text{ nm} = 10^{-9} \text{ meters} \)
- \( 1 \text{ µm} = 10^{-6} \text{ meters} \)

### Step 3: Determine the typical wavelength of X-rays
- The wavelength of X-rays is generally around \( 1 \text{ nm} \).

### Step 4: Express both units in meters
- Therefore, we can express \( P \) and \( Q \) in meters:
- \( P = 1 \text{ nm} = 10^{-9} \text{ m} \)
- \( Q = 1 \text{ µm} = 10^{-6} \text{ m} \)

### Step 5: Calculate the ratio \( \frac{P}{Q} \)
- Now we can find the ratio:
\[ \frac{P}{Q} = \frac{10^{-9} \text{ m}}{10^{-6} \text{ m}} \]

### Step 6: Simplify the expression
- Simplifying the fraction:
\[ \frac{P}{Q} = 10^{-9} \div 10^{-6} = 10^{-9 + 6} = 10^{-3} \]

### Step 7: Conclusion
- Thus, the ratio \( \frac{P}{Q} = 10^{-3} \).

### Final Answer
- The correct option is \( 10^{-3} \).

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