The concept of thermionic emission is the basis of modern X-ray tubes, which are

Question

The concept of thermionic emission is the basis of modern X-ray tubes, which are the workhorse of a medical X-ray image. In this process a filament (a piece of metal in a vacuum) is heated by the application of electrical current. The heat (energy) is transferred to the 'free' electrons of the metal which allow some electrons to escape from the surface. After a short period of operation the filament has lost enough electrons to give it an overall charge of 9.50 x107 C. How many electrons, ne, has the filament lost? If the filament is 1.25 g of tungsten, what fraction of electrons, er, does this represent? (HINT: The atomic number of tungsten is 74.0, the atomic weight is 183.8 g/mol and Avogadro's constant-6.02% 1023 1 fmol.) Number Number

Explanation / Answer

(a) Charge of an electron (e)= 1.6*10-19 C
Total charge lost by the filament = 9.5*10-7 C
Therefore no of electron lost
ne = total charge/ charge of an electron
= 9.5*10-7 /  1.6*10-19
ne= 5.94*1012 electrons
This would be the no. of electrons lost by the filament.
(b) Now atomic weight of the tungsten = 183.8 g/mol
it means that
183.8 g = 1 mol
1g = (1/183.8) mol
1.25 g = 1.25*(1/183.8) mol
1 mol = 6.02*1023 atoms
1.25 g = 1.25*(1/183.8)*(6.02*1023) atoms
1.25 g = 4.094*1021 atoms
Now, atomic no. of tungsten = 74 that means
1 atom = 74 electron , therefore
1.25 g = 4.094*1021*74 = 3.029*1023 electrons
Now,
fraction(ef) = (answer in part a) / no. of electrons in 1.25g
= 5.94*1012 /3.029*1023
fraction (ef) = 1.961*10-11

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