X-Ray Production in Beiser's Physics Textbook: Typo or Not?

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In summary, in the modern physics textbook 6/E by Arthur Beiser, the formula for x-ray production is given as (lambda minimum) = 1.24*10^(-6)/V V*m. This raises the question of whether this is a typo, as lambda (wavelength) is measured in meters, while V (voltage) is measured in volts. However, this formula is correct as it refers to the minimum wavelength of x-rays produced by accelerating electrons through a voltage V and hitting a target. The value of hc/e, equivalent to 1.24*10^(-6) Vm, is used to calculate the minimum wavelength.
  • #1
asdf1
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in my modern physics textbook 6/E by arthur beiser,
the formula for x-ray production is written as
(namdamin)=1.24*10^(-6)/V V*m
is that a typo? how can namda have units of V*m?
 
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  • #2
Perhaps it would help if you explained exactly what you are talking about!

As far as I know "x-ray production" doesn't have units! What exactly does
"nambdamin" mean? (Was that supposed to be "lambda"?) Oh, and what is V? volts?
 
  • #3
x-ray production doesn't have units?
jeepers~
i must be misunderstanding modern physics...
:P
i don't know how to type the symbols, but yes, "nambda min" means the "lambda" minimun...
V stands for volts...
 
  • #4
the second V (that's multiplied by meters) is a UNIT, Volts.
But the first V (that you divide by) is a VARIABLE ... Voltage.

These are NOT the same thing, but the units cancel.

"the lamda minimum ..."
lamda of WHAT? V of WHAT?
 
  • #5
asdf1 said:
in my modern physics textbook 6/E by arthur beiser,
the formula for x-ray production is written as
(namdamin)=1.24*10^(-6)/V V*m
is that a typo? how can namda have units of V*m?
You are talking about the minimum wavength of x-rays produced by accelerating electrons through a voltage V and slamming them against a target. Naturally, the maximum energy of an x-ray will be the final KE of the electron before it hits the target.

That gives

[tex]KE(electron) = e*V = \frac{hc}{\lambda_{min}} [/tex]
[tex]\implies~ \lambda_{min} = \frac{hc}{eV} = \frac {hc}{e} \cdot \frac{1}{V} [/tex]

The quantity [itex]hc/e[/itex] has a value of [itex]1.24 *10^{-6}~Vm [/itex]

When you divide by the units of the applied voltage V (ie: volts), you are left with units of meters, the correct unit for a wavelength !
 
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  • #6
thank you very much! :)
 

1. Is "X-Ray Production" a typo in Beiser's Physics textbook?

No, "X-Ray Production" is not a typo in Beiser's Physics textbook. It is a term used to describe the production of X-rays through various methods.

2. How are X-rays produced according to Beiser's Physics textbook?

According to Beiser's Physics textbook, X-rays can be produced through two main methods: bremsstrahlung (braking radiation) and characteristic radiation.

3. What is bremsstrahlung or braking radiation?

Bremsstrahlung or braking radiation is a type of X-ray production where high-speed electrons are decelerated by a target material, causing them to emit X-rays.

4. What is characteristic radiation?

Characteristic radiation is a type of X-ray production where electrons from an outer shell of an atom are knocked out by high-speed electrons, causing the atom to emit X-rays as the outer shell is filled by electrons from higher energy levels.

5. Can X-rays be produced through any other methods?

Yes, X-rays can also be produced through other methods such as synchrotron radiation, nuclear reactions, and laser-induced plasma. However, bremsstrahlung and characteristic radiation are the most commonly used methods in medical and industrial settings.

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