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

Question

The concept of thermionic emission is the basis of modem 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 1.100 times 10^-6. How many electrons, n_e, has the filament lost? If the filament is 2.15 g of tungsten, what fraction of electrons, e_f. does this represent? (The atomic number of tungsten is 74.0. the atomic weight is 183.8 g/mol and Avogadro's constant = 6.02 times 10^23 1/mol.)

Explanation / Answer

Total charge is given by:

Q = n*e

n = Q/e

Q = 1.1*10^-6 C

e = 1.6*10^-19 C

Total number of electrons after some time = 1.1*10^-6/(1.6*10^-19) = 6.875*10^12 electrons

electron lost will be = ne = 6.875*10^12 electrons

Now Initially total electrons present will be

In 2.15 gm of tungsten, no. of electrons will be:

Total elctrons = Na*A*w/Mw

= 6.023*10^23*74*2.15/183.8 = 5.213*10^23 electrons

fraction lost = ne/Total electrons

ef = 6.875*10^12/(5.213*10^23) = 1.32*10^-11

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