Calculation of the least value of PD needed to produce x-rays

[Asmaa Mohammad]

Homework Statement

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In my excercise book, I was given a typical diagram as that in Fig (6-7) above.
And the problem statement says:
The diagram presents the x-ray spectrum produced by Coolidge tube. Determine the least potential difference needed to produce the characteristic radiation.

Homework Equations

E= hƒ = hc/λ where: h is Planck's constant, ƒ is the frequency, c is light speed and λ is the wavelength)
K.E= eV

The Attempt at a Solution

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I really don't know how to start in this, because the diagram doesn't appear to be precise, I mean I don't know actually the precise shortest wavelength where the characteristic radiation appears in the diagram, would it be 0.07nm?!

If it would be 0.07nm, I will do this:

E=hc/λ=(6.625*10^-34)* (3*10^8)/ (0.07*10^-9)
=2.8*10^-15 j
Then,
eV= E -----> V=E/e = (2.8*10^-15)/ (1.6*10^-19)
=17.5 kV.

But I don't think my approach is correct, so I am waiting your help.

 

[kuruman]

If it would be 0.07nm

Can you come up with abetter estimate? λ_m is to the left of the 0.04 nm mark.

But I don't think my approach is correct ...

What makes you say this?

 

[Asmaa Mohammad]

Can you come up with abetter estimate? λ_m is to the left of the 0.04 nm mark

OK, but it is λm of the bremsstrahlung radiation not the characteristic, isn't it?
I say that my approach is wrong because I don't actually understand the problem or how to start.

 

[kuruman]

Y

OK, but it is λ_m of the bremsstrahlung radiation not the characteristic, isn't it?

Correct. Now suppose you have an electron accelerated to energy E. Consider two cases after it slams into the target: (1) it produces a single photon of energy E; (2) it produces two photons each with energy E/2. In which case is the wavelength shorter?

 

[Asmaa Mohammad]

Y

Correct. Now suppose you have an electron accelerated to energy E. Consider two cases after it slams into the target: (1) it produces a single photon of energy E; (2) it produces two photons each with energy E/2. In which case is the wavelength shorter?

The photon in case (1) will have a shorter wavelength because it has a larger frequency. But what is the relation of this with what we try to get?

 

[kuruman]

But what is the relation of this with what we try to get?

Note that we are trying to get the potential difference (1) through which the electron is accelerated.
Note that (1) is related to the energy of the electron (2).
Note that, if (2) goes into producing a single photon, this photon has the minimum wavelength λ_m (3).
Note that you can read (3) off the plot.

 

[Asmaa Mohammad]

OK. But let me say something here, and I hope you get my point of view
The accelerated electron through the PD, can produce either a bremsstrahlung spectrum or a characteristic spectrum, right? The bremsstrahlung has its own minimum wavelength, the characteristic spectrum has its own minimum wavelength too, right?
The minimum wavelength of the bremsstrahlung can be estimated to be 0.035nm whilst the minimum wavelength of the characteristic is (in my opinion) directly below the left peak of the characteristic line spectrum, e.g., 0.07nm.
Are those points correct?

 

[kuruman]

The accelerated electron through the PD, can produce either a bremsstrahlung spectrum or a characteristic spectrum, right?

It is more appropriate to think that the accelerated electron produces a certain number of photons, not a spectrum. The sum of the energies of these photons must equal the initial energy of the electron. The spectrum is generated by looking at the distribution of a whole lot of photons produced by a whole lot of electrons.

 

[Asmaa Mohammad]

It is more appropriate to think that the accelerated electron produces a certain number of photons, not a spectrum. The sum of the energies of these photons must equal the initial energy of the electron. The spectrum is generated by looking at the distribution of a whole lot of photons produced by a whole lot of electrons.

OK, you are right. But still I don't know the answer of my question.

 

[kuruman]

Please read post #6. It has all the hints you need. Connect the dots.

 

[Asmaa Mohammad]

this photon has the minimum wavelength λm (3).

I don't know which wavelength (0.035nm or 0.07nm) is to be used to solve the problem.

 

[kuruman]

I don't know which wavelength (0.035nm or 0.07nm) is to be used to solve the problem.

Use the minimum wavelength. Minimum means smallest. Which is smaller, 0.035 nm or 0.07 nm?