Calculate vmax and voltage from X-ray distribution function

In summary, the X-ray intensity distribution function for an X-ray lamp is given on the figure. The maximum velocity of the electrons can be calculated using the formula v = sqrt [2h(c/λ)/m], which gives a value of 1.1 x 10^7 m/s. However, the correct answer is 1.5 x 10^7 m/s. The potential difference under which the lamp is operating can be calculated using the formula ΔV = qΔV, where q is the charge and ΔV is the potential difference. This gives a value of 1.5 x 10^-15 V.
  • #1
VH1
2
0

Homework Statement


The X-ray intensity distribution function for an X-ray lamp is
given on the figure. What is the maximum velocity of the electrons? What is the potential difference under which the lamp is operating? Figure: http://imgur.com/01kCBc8
01kCBc8.png


Homework Equations


Kmax = 0.5m(vmax)^2
Kmax = hf - work function
λ = c/f
c = speed of light = 3 x 10^8 m/s
Peak wavelength (from the figure) = 3.5 x 10^-9 m
h = Planck's constant = 6.63 x 10^-34
m = mass of electron = 9.11 x 10^-31

The Attempt at a Solution


Doubt I'm starting at the right place.
0.5mv^2 = hf (work function??)
0.5mv^2 = h(c/λ)
v = sqrt [2h(c/λ)/m]
v = 1.1 x 10^7 m/s
Given answer is 1.5 x 10^7 m/s

As for the potential difference, I have no idea how to calculate it.
 
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  • #2
Hi VH1,

Welcome to Physics Forums!

X-Ray production isn't quite the same thing as the photoelectric effect. In this case electrons are stopped by a target and shed their energy in the form of photons.

Looking at the intensity distribution, which wavelength on the curve represents the highest energy photons (not the total intensity of emitted photons, but the highest photon energy)?

For the potential difference, how much energy does a charge gain by "falling through" a given potential difference? What's the formula?
 
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Likes VH1
  • #3
Thanks gneill for the warm welcome and help - I managed to work out both questions with that.

Cheers
 

What is the process for calculating vmax and voltage from an X-ray distribution function?

The process for calculating vmax and voltage from an X-ray distribution function involves several steps. First, the X-ray distribution function must be plotted on a graph. Then, the peak of the curve, which represents the maximum intensity, can be identified. Next, the corresponding x-axis value at the peak is the value for vmax. Finally, the voltage can be calculated using the equation V = (hc)/(λmax), where h is Planck's constant, c is the speed of light, and λmax is the wavelength at the peak intensity.

What is the significance of calculating vmax and voltage from an X-ray distribution function?

Calculating vmax and voltage from an X-ray distribution function allows for the determination of the maximum kinetic energy of electrons emitted from a material when exposed to X-rays. This information is crucial in understanding the electronic structure and properties of the material, which has implications in various fields such as materials science, chemistry, and physics.

Are there any limitations to calculating vmax and voltage from an X-ray distribution function?

Yes, there are some limitations to this calculation. One limitation is that the X-ray distribution function may not accurately represent the true electron energy distribution in the material. This can be caused by factors such as instrumental broadening, which can distort the shape of the curve. Additionally, this calculation assumes a simple one-dimensional model and may not accurately reflect the complexities of the material's electronic structure.

Can this calculation be applied to all materials?

No, this calculation is primarily used for crystalline materials. The X-ray distribution function is a result of the periodic arrangement of atoms in a solid, which is a characteristic of crystalline materials. Amorphous or disordered materials do not exhibit this periodicity, so this calculation would not be applicable.

Are there any alternative methods for determining vmax and voltage?

Yes, there are alternative methods for determining vmax and voltage. One method is using photoelectron spectroscopy, which involves bombarding a material with X-rays and measuring the kinetic energy of emitted electrons. Another method is using electron energy loss spectroscopy, which measures the energy lost by electrons as they pass through a material. Both of these methods provide more direct measurements of electron energies and can be used to verify the results obtained from the X-ray distribution function.

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