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 × 10-7 C. How many electrons, ne, has the filament lost? If the filament is 2.30 g of tungsten, what fraction of electrons, ef, 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/mol.)

Explanation / Answer

The charge of single electron is-1.6*10^-19C
the total charge lost is-1.100*10^-6
so the no of electron lost=(9.5*10^-7)/(1.6*10^-19)=5.94*10^ 12

the atomic weight of tungsten is 183.8 g/mol. So 183.8 gm tungsten contain Avogadros number(6.023*10^23) of atoms.
then 2.3 gm of tungsten will contain (6.023*10^23)*2.3/183.8=7.536 *10^21no of atom.

Again 1 tungsten atom contain 74 no of electron.
so total no of electron=74* 7.536*10^21= 5.576*10^23

now %of electron lost=5.94 *10 ^12 *100/5.576^ 23 =1.07 *10 ^9%

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