Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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P If the Operating Potential in an X-ray Tube is Increased by 1%, by What Percentage Does the Cutoff Wavelength Decrease? - Physics

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Question

If the operating potential in an X-ray tube is increased by 1%, by what percentage does the cutoff wavelength decrease?

(Use Planck constant h = 6.63 × 10-34 Js= 4.14 × 10-15 eVs, speed of light c = 3 × 108 m/s.)

Solution

Let  `lambda` be the cut off wavelength and V be the operating potential in the X-ray tube.
Then, `lambda = (hc)/V`

Here,
h = Planck's constant
c = Speed of light

If the operating voltage is increased by 1%, then the new operating voltage (V') will be given by

`V^' = V + 1/100 xx V`

`V^' = 1.01  "V"`

Cut off wavelength (`lambda^'`) on increasing the operating voltage is given by

`lambda^' = (hc)/(1.01  "V") = lambda/1.01`

`therefore lambda^' - lambda = 0.01/1.01lambda`

Percentage change in the wavelength is given by

`(0.01lambda)/(1.01 xx lambda) xx 100 = 1/1.01`

= 0.9901

=1 (approx.)

  Is there an error in this question or solution?

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Solution P If the Operating Potential in an X-ray Tube is Increased by 1%, by What Percentage Does the Cutoff Wavelength Decrease? Concept: Electromagnetic Spectrum.
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