X-rays with an energy of 400 kev undergo compton scattering with a target. if the scattered x-rays are detected at \theta = 30^{\circ}θ=30 ∘ relative to the incident x-rays, what is the energy of the recoiling electron? [assume that energy is conserved in this interaction]

Explanation:

Photons have momentum, this was proved by he American physicist Arthur H. Compton after his experiments related to the scattering of photons from electrons (Compton Effect or Compton Shift). In addition, energy and momentum are conserved in the process.

In this context, the Compton Shift in wavelength when the photons are scattered is given by the following equation:

    (1)

Where:

is a constant whose value is given by , being the Planck constant, the mass of the electron and the speed of light in vacuum.

the angle between incident phhoton and the scatered photon.

We are told the scattered X-rays (photons) are detected at :

  (2)

  (3)

Now, the initial energy of the photon is given by:

     (4)

From this equation (4) we can find the value of :

   (5)

   (6)

Knowing the value of and , let's find :

Then:

 (7)

 (8)

Knowing the wavelength of the scattered photon  , we can find its energy :

   (9)

   (10) This is the energy of the scattered photon

So, if we want to know the energy of the recoiling electron , we have to calculate all the energy lost by the photon, which is:

 (11)

Finally we obtain the energy of the recoiling electron:

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

because growing process had stoped after 4-5 year