Electrons with energy `80 keV` are incident on the tungsten target of an X - rays tube , k- shell electrons of tungsten have `72.5 keV` energy X- rays emitted by the tube contain only

Explanation

To solve the problem, we need to analyze the situation where electrons with energy of 80 keV are incident on a tungsten target, and we need to determine the characteristics of the X-rays emitted from this interaction.

### Step-by-Step Solution:

1. **Identify the Energy of Incident Electrons**:
The energy of the incident electrons is given as \( E = 80 \, \text{keV} \).

2. **Identify the Binding Energy of K-shell Electrons**:
The binding energy of the K-shell electrons in tungsten is given as \( E_k = 72.5 \, \text{keV} \).

3. **Determine if K-shell Electrons Can Be Ejected**:
Since the energy of the incident electrons (80 keV) is greater than the binding energy of the K-shell electrons (72.5 keV), the incident electrons can knock out K-shell electrons from the tungsten atoms.

4. **Calculate the Minimum Wavelength of the X-rays**:
The energy of the emitted X-rays can be calculated using the formula relating energy and wavelength:
\[ E = \frac{hc}{\lambda} \]
Rearranging this gives:
\[ \lambda = \frac{hc}{E} \]
Here, \( h \) (Planck's constant) is approximately \( 4.135667696 \times 10^{-15} \, \text{eV s} \) and \( c \) (speed of light) is approximately \( 3 \times 10^8 \, \text{m/s} \).

5. **Convert Energy to Joules**:
First, we convert the energy from keV to joules:
\[ E = 80 \, \text{keV} = 80 \times 10^3 \, \text{eV} = 80 \times 10^3 \times 1.6 \times 10^{-19} \, \text{J} = 1.28 \times 10^{-14} \, \text{J} \]

6. **Calculate the Wavelength**:
Now substituting the values of \( h \), \( c \), and \( E \) into the wavelength formula:
\[ \lambda = \frac{(4.135667696 \times 10^{-15} \, \text{eV s})(3 \times 10^8 \, \text{m/s})}{80 \times 10^3 \times 1.6 \times 10^{-19} \, \text{J}} \]
After calculating, we find:
\[ \lambda \approx 0.155 \, \text{Å} \]

7. **Conclusion**:
The X-rays emitted by the tube contain a continuous X-ray spectrum with a minimum wavelength of approximately \( 0.155 \, \text{Å} \).