X rays

Finishing Option G

X-ray production

We have seen that an accelerating charge must emit energy in the form of EM radiation. If this acceleration is large enough, the wavelength of light emitted will lie in the X-ray region of the spectrum.

X-Ray Production

X-Rays are produced when electrons accelerated by a high voltage strike a metal target.

The electrons are brought to rest by the collisions with the atoms of the target.

This leads to a whole range of wavelengths

Coolidge Tube

X-Ray Production: The continuous spectrum

These wavelengths vary because all the electron’s energy may not be transferred in the collision.

If all the electron’s energy is converted into a photon, this photon will have the largest possible energy. This corresponds to a MINIMUM WAVELENGTH

KEeV

KEqV

KEEQ

Minimum wavelength

The energy of the incoming electron is

This will be the energy of the photon, E=hf

eV

hc

hceV

hfeV

X-Ray Production: The continuous spectrum

The minimum wavelength only depends on the accelerating voltage.

Minimum wavelength

If the electron only converts a fraction of its kinetic energy in the collision, then the wavelengths will be longer.

X-Ray Production: The continuous spectrum

X-Rays: Characteristic X-Rays

The graph we have seen is only a part of the story.

What are these characteristic lines all about?

X-Rays: Characteristic X-Rays

If we change the accelerating voltage we get:

They are not affected by the accelerating voltage.

They are dependant on the target metal.

X-Rays: Characteristic X-Rays

If an electron has the right energy, it can knock an electron from the target out of the lowest energy level (the K shell).

ee eAn electron in a higher energy of the atom will fall to replace the electron. The energy gap corresponds to the energy of an X-ray.

Examples

Operating an X-ray tube:Strictly speaking, the Bohr model does not

apply to multiple-electron atoms, but it can be used to make estimates. Use the Bohr model to estimate the minimum energy that an incoming electron must have to knock a K-shell electron entirely out of an atom in a platinum target in a X-ray tube.

Answer

E1 = -(13.6eV)Z^2/n^2 = -8.27 x 10^4 eV

The electron must be removed (up to an E level of 0 eV) so 8.27x 10^4eV is required.

Thus a voltage of 8.27x 10^4 V is required.