#### Question

When 40 kV is applied across an X-ray tube, X-ray is obtained with a maximum frequency of 9.7 × 10^{18} 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 × 10^{8} m/s.)

#### Solution

Given:-

Potential applied to the X-ray tube, V = 40 kV

Frequency of the X-ray, v = 9.7 × 10^{18} 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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#### APPEARS IN

Solution Div » P 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. Concept: Electromagnetic Spectrum.