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Question
When 40 kV is applied across an X-ray tube, X-ray is obtained with a maximum frequency of 9.7 × 1018 Hz. Calculate the value of Planck constant from these data.
(Use Planck constant h = 6.63 × 10-34 Js= 4.14 × 10-15 eVs, speed of light c = 3 × 108 m/s.)
Solution
Given:-
Potential applied to the X-ray tube, V = 40 kV
Frequency of the X-ray, v = 9.7 × 1018 Hz
Wavelength (`lambda`) is given by
`lambda = (hc)/(eV)`
Here,
h = Planck's constant
c = Speed of light
`e = 1.6 xx 10^-19`
`therefore lambda = (hc)/(eV)`
`⇒ lambda/c = h/(eV)`
`⇒ 1/v = h/(eV) ..................(∵ v = c/lambda)`
`⇒ h = (eV)/v`
`⇒ h = (40 xx 10^3)/(9.7 xx 10^18) xx e`
`⇒ h = 4.12 xx 10^-15 "eVs"`
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