The distance between two consecutive atoms of the crystal lattice is 1.227Å. The maximum order of diffraction of electrons accelerated through `10^(4) volt will be -

Options

A. 10
B. `1//10`
C. 100
D. `1//100`

Answer

To solve the problem of finding the maximum order of diffraction of electrons accelerated through \(10^4\) volts, we can follow these steps:

### Step 1: Understand the relationship between wavelength and accelerating voltage
The wavelength (\(\lambda\)) of electrons can be calculated using the formula:
\[ \lambda = \frac{12.27}{\sqrt{V}} \text{ Å} \]
where \(V\) is the accelerating voltage in volts.

### Step 2: Substitute the given voltage into the formula
Given that the accelerating voltage \(V = 10^4\) volts, we can substitute this value into the formula for wavelength:
\[ \lambda = \frac{12.27}{\sqrt{10^4}} \text{ Å} \]
Calculating \(\sqrt{10^4}\):
\[ \sqrt{10^4} = 10^2 = 100 \]
Now substituting this back into the wavelength formula gives:
\[ \lambda = \frac{12.27}{100} \text{ Å} = 0.1227 \text{ Å} \]

### Step 3: Use the diffraction condition to find the maximum order
The condition for diffraction is given by:
\[ n \lambda = d \sin \theta \]
where \(n\) is the order of diffraction, \(d\) is the distance between two consecutive atoms in the crystal lattice, and \(\sin \theta\) can be at most 1 for maximum diffraction.

Given that the distance \(d = 1.227 \text{ Å}\), we can rearrange the equation for maximum order \(n\):
\[ n = \frac{d}{\lambda} \]
Substituting the values we have:
\[ n = \frac{1.227 \text{ Å}}{0.1227 \text{ Å}} \]

### Step 4: Calculate the maximum order of diffraction
Performing the division:
\[ n = \frac{1.227}{0.1227} \approx 10 \]

### Conclusion
Thus, the maximum order of diffraction of electrons accelerated through \(10^4\) volts is:
\[ \boxed{10} \]