If the shortest wavelength produced by an X-ray tube is 0.46 nm, what is the voltage applied to the tube? (Answer: 2.7 kV)



Given:


Wavelength = λ = 0.46 nm =  0.46 ｘ 10⁻⁹ m

∴ Plank's Constant = h =  6.62 ｘ 10⁻³⁴ m² kg s⁻¹

∴ Charge on the electron = e = 1.6 ｘ 10⁻¹⁹ C

∴ Velocity of light  = c = 3 ｘ 10⁸ m s⁻¹



To Find:


The voltage supplied = V =  ?


Solution:

We know that 

h`\f_{max}` = Ve

where `\f_{max}` = `\frac {c}{λ_{min}}`

Thus

h`\frac {c}{λ_{min}}` = Ve

or

V = `\frac {hc}{eλ_{min}}`

by putting values

V = `\frac {6.62 ｘ 10⁻³⁴ m² kg s⁻¹ ｘ 3 ｘ 10⁸ m s⁻¹}{1.6 ｘ 10⁻¹⁹ C ｘ 0.46 ｘ 10⁻⁹ m}`

V = `\frac {19.86 ｘ 10⁻²⁶ m³ kg s⁻² }{0.736 ｘ 10⁻²⁸ C m}`

V = 26.984 ï½˜ 10² V

V = 2.698 ｘ 10³ V

or

V = 2.698 kV -----------------Ans.


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