Which one of the following statements concerning the cutoff wavelength typically exhibited in x-ray spectra is true?

Options

A. The cutoff wavelength depends on the target material
B. The cutoff wavelength depends on the potential difference across the x-ray tube
C. The cutoff wavelength is independent of the energy of the incident electrons
D. The cutoff wavelength occurs because of the mutual shielding effects of K-shell electrons

Answer

To determine which statement about the cutoff wavelength in X-ray spectra is true, we can follow these steps:

### Step 1: Understand the Concept of Cutoff Wavelength
The cutoff wavelength in X-ray spectra refers to the maximum wavelength of X-rays that can be produced by an X-ray tube. This wavelength is inversely related to the energy of the X-rays generated.

### Step 2: Relate Cutoff Wavelength to Energy
The energy (E) of X-rays is related to their wavelength (λ) by the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant,
- \( c \) is the speed of light,
- \( \lambda \) is the wavelength.

From this equation, we can see that as the energy increases, the wavelength decreases, which means the cutoff wavelength is affected by the energy of the X-rays.

### Step 3: Consider the Role of Accelerating Voltage
The energy of the X-rays generated in an X-ray tube is directly proportional to the accelerating voltage (V) applied across the tube. The higher the voltage, the greater the energy of the emitted X-rays, leading to a shorter cutoff wavelength.

### Step 4: Analyze the Given Options
Now, we need to evaluate the statements provided in the question. The key point is that the cutoff wavelength primarily depends on the accelerating voltage rather than the target material used in the X-ray tube.

1. **Option 1**: Cutoff wavelength depends on the target material. (This is incorrect; it primarily depends on the voltage.)
2. **Option 2**: Cutoff wavelength depends on the accelerating voltage. (This is correct; it directly relates to the energy of the X-rays.)
3. **Option 3**: Cutoff wavelength is independent of the voltage. (This is incorrect; it is dependent on the voltage.)
4. **Option 4**: Cutoff wavelength is constant for all X-ray tubes. (This is incorrect; it varies with the voltage.)

### Step 5: Conclusion
Based on the analysis, the correct statement concerning the cutoff wavelength in X-ray spectra is:
**Option 2: Cutoff wavelength depends on the accelerating voltage.**