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Using a beam of electrons accelerated in an X-ray tube, we wish to knock an electron out of the shell of given element in a target. Section \(7.8\) gives the energies in a hydrogen like atom as . Z2(-13.6eV/n2)Assume that for fairly high Z , aK-shell electron can be treated as orbiting the nucleus alone.

(a) A typical accelerating potential in an X-ray tube is50kV . In roughly how high aZcould a hole in the K -shell be produced?

(b) Could a hole be produced in elements of higher Z?

Short Answer

Expert verified

(a) The resultant answer is Z=61

(b) Yes, for higher.

Step by step solution

01

Given data

Accelerated potential, V=50,000V

02

Concept of Determinant

The energy of electron innth-orbit:

The energy KE which an object of charge q gains by passing through the potential difference VisKE=qV

03

Determine the energy

(a)

If the accelerating potential is V=50kV, then the energy of the accelerated electron would beE=50keV .

This electron can 'knock out' an electron in the shell with an energy of E1=-50keV.

By Eq. (1), find the atomic number Z as (note that n=1 for the K shell).

Z=50103eV13.6eVZ60\hfill

04

Determine the energy

(b)

If we were to strike an atom with higher atomic number than the one, we've calculated z=60 , we could make a hole but the level must be higher than n=1(the K shell).

If n was not larger, then the absolute value of the orbiting electron would be greater (see Eq. (1)) and the value of the accelerating potential would not be great enough.

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