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 the electrons hit the phosphor, we need to use the equation relating energy and wavelength:
E = hc/λ
Where:
E is the energy of the X-ray photon
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)
λ is the wavelength of the X-ray photon
The energy of the X-ray photon can be calculated using the formula:
E = qV
Where:
q is the electron charge (1.6 x 10^-19 C)
V is the voltage (20,000 V)
Now, let's substitute the values into the equation:
E = (1.6 x 10^-19 C) * (20,000 V)
E = 3.2 x 10^-15 J
Now, we can rearrange the first equation to solve for the wavelength:
λ = hc/E
Substituting the values:
λ = (6.626 x 10^-34 J·s) * (3.0 x 10^8 m/s) / (3.2 x 10^-15 J)
λ ≈ 6.19 x 10^-11 meters
Therefore, the minimum wavelength for the continuous X-ray spectrum produced when the electrons hit the phosphor is approximately 6.19 x 10^-11 meters.