A television tube operates at 20,000V. What is min wavelength for the continuous x-ray spectrum produced when the electrons hit the phosphor?
To find the minimum wavelength for the continuous X-ray spectrum produced when electrons hit the phosphor in a television tube, we need to use the following formula:
λ_min = hc / eV
Where:
λ_min represents the minimum wavelength
h is Planck's constant (6.626 x 10^-34 J·s)
c is the speed of light (3.0 x 10^8 m/s)
e is the elementary charge (1.602 x 10^-19 C)
V is the voltage (20,000 V)
Let's substitute the given values into the formula:
λ_min = (6.626 x 10^-34 J·s * 3.0 x 10^8 m/s) / (1.602 x 10^-19 C * 20,000 V)
Now, let's calculate it:
λ_min = (1.9888 x 10^-25 J·m) / (3.204 x 10^-14 C·V)
Simplifying it further:
λ_min = 6.19 x 10^-12 m
Hence, the minimum wavelength for the continuous X-ray spectrum produced when the electrons hit the phosphor in a television tube is approximately 6.19 x 10^-12 meters.