To determine the minimum wavelength of the X-ray produced by an X-ray tube with an applied voltage of 50 kV, we can use the formula:
λ = hc / eV
Where:
λ is the wavelength of the X-ray
h is the Planck constant (6.626 x 10^-34 J s)
c is the speed of light (3.00 x 10^8 m/s)
e is the elementary charge (1.602 x 10^-19 C)
V is the applied voltage (50 kV = 50 x 10^3 V)
Plugging in the values:
λ = (6.626 x 10^-34 J s * 3.00 x 10^8 m/s) / (1.602 x 10^-19 C * 50 x 10^3 V)
λ = (1.9878 x 10^-25 J m) / (8.01 x 10^-15 C)
λ ≈ 2.48 x 10^-11 m
Therefore, the minimum wavelength of the X-ray produced by an X-ray tube with an applied voltage of 50 kV is approximately 2.48 x 10^-11 meters.
