The cut-off wavelength when a potential difference of 25 kV is applied to an X-ray tube, is

Solution to the Problem: The Cut-off Wavelength When a Potential Difference of 25 kV is Applied to an X-ray Tube

Step 1: Formula for Cut-off Wavelength

The cut-off wavelength is the minimum wavelength of X-rays produced when a potential difference V is applied to the X-ray tube. It can be calculated using the following formula:

Energy equation:

E = &frac{hc}{λ}

Where:

- E is the energy of the X-ray photon, 
- h is Planck's constant (6.626 × 10^-34 J·s), 
- c is the speed of light (3 × 10⁸ m/s), 
- λ is the wavelength of the X-ray.

The energy of the photon is related to the applied potential difference V by:

E = eV

Where:

- e is the charge of an electron (1.602 × 10^-19 C),
- V is the potential difference applied.

Step 2: Calculation

Energy from the Potential Difference:

Given that the potential difference is 25 kV, we can calculate the energy as follows:

E = eV = (1.602 × 10^-19 C) × (25 × 10³ V) = 4.005 × 10^-15 J

Wavelength of the X-ray Photon:

Using the energy and the formula for wavelength, we can now calculate the wavelength:

λ = &frac{hc}{E}

Substituting the known values:

λ = &frac{(6.626 × 10^-34 J·s) × (3 × 10⁸ m/s)}{4.005 × 10^-15 J}

λ ≈ 4.96 × 10^-11 m = 0.496 nm = 0.496 Å

Final Answer:

The cut-off wavelength when a potential difference of 25 kV is applied to the X-ray tube is approximately 0.496 Å.