The shorted wavelength of X- rays emitted from an X- rays tube depends on

Options

A. the current in the tube
B. the voltage applied to the tube
C. the nature of the gas in the tube
D. the atomic number of the target meterial

Explanation

To solve the question regarding the shortest wavelength of X-rays emitted from an X-ray tube, we can follow these steps:

### Step 1: Understand the relationship between energy and wavelength
The energy (E) of the emitted X-rays is related to their frequency (ν) by the equation:
\[ E = hν \]
where \( h \) is Planck's constant.

### Step 2: Relate energy to wavelength
We can express frequency in terms of wavelength (λ) using the equation:
\[ ν = \frac{c}{λ} \]
where \( c \) is the speed of light. Substituting this into the energy equation gives us:
\[ E = h \frac{c}{λ} \]
Rearranging this, we find:
\[ λ = \frac{hc}{E} \]

### Step 3: Consider the energy source in the X-ray tube
In an X-ray tube, the energy of the emitted X-rays is primarily determined by the voltage (V) applied to the tube. The energy can be expressed in electronvolts (eV) as:
\[ E = eV \]
where \( e \) is the charge of an electron.

### Step 4: Substitute energy into the wavelength equation
Substituting \( E = eV \) into the wavelength equation, we get:
\[ λ = \frac{hc}{eV} \]
This shows that the wavelength (λ) is inversely proportional to the voltage (V) applied to the tube.

### Step 5: Analyze the options
Now, let's analyze the options given in the question:
1. The current in the tube - This does not directly affect the wavelength.
2. The wattage applied to the tube - This is related to power but does not directly determine the shortest wavelength.
3. The nature of the gas in the tube - This does not affect the wavelength of X-rays.
4. The atomic number of the target material - While it affects the intensity and quality of X-rays, it does not directly determine the shortest wavelength.

### Conclusion
From our analysis, we conclude that the shortest wavelength of X-rays emitted from an X-ray tube primarily depends on the voltage applied to the tube.

**Final Answer: The shortest wavelength of X-rays emitted from an X-ray tube depends on the voltage applied to the tube.**

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