In order to make X-rays, a copper target is bombarded with high-energy electrons

Question

In order to make X-rays, a copper target is bombarded with high-energy electrons. The electrons are energetic enough to remove a core electron instead of a valence electron. When the core electron is removed, other higher energy electrons fall to the lower energy state and release X-ray radiation.

a) If the X-ray released has a wavelength of 1.54E-10m, what is the energy in joules of the released X-ray? 1.29 x 10-15 J

b) In order to create the energetic electron, the electron is accelerated in an electric field. The kinetic energy of the electron equals the product of the voltage difference and the charge of the electron (1 volt*coulomb = 1 J = 1 kg*m2*s-2). What is the kinetic energy of the electron if it was accelerated in a field of 30,000V? 4.8 x 10-15 kgm2s-2

c) How much energy does it take to remove a core electron?

Explanation / Answer

a) Given that wavelength = 1.54 x 10-10 m

Energy E = hc /

h = planck's constant = 6.626 x 10-34 J.s

c = velocity of light = 3 x 108 m/s

Hence,

  E = hc /

    =  (6.626 x 10-34 J.s) (3 x 108 m/s) / (1.54 x 10-10 m)

   = 1.29 x 10-15 J

E = 1.29 x 10-15 J

Therefore,

Energy of the released X-ray = 1.29 x 10-15 J

b)   Given that kinetic energy of the electron equals the product of the voltage difference and the charge of the electron.

Therefore,

kinetic energy of the electron = voltage difference x charge of the electron

                                            = 30,000 V x 1.602 x 10-19 C

                                            = 4.8 x 10-15 kgm2s-2

                                            = 4.8 x 10-15 J

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