When the voltage applied to an X-ray tube increased from V 1 = 15.5 kV to V 2 = 31 kV , the wavelength interval between the K α line and the cut-off wavelength of the continuous X-ray spectrum increas

Question

When the voltage applied to an X-ray tube increased from $V_{1} = 15.5 kV$ to $V_{2} = 31 kV$ , the wavelength interval between the $K_{α}$ line and the cut-off wavelength of the continuous X-ray spectrum increases by a factor of $1.3$ . Identify the element.

(Take: $h c = 1240 eV nm$ and $R = 1 \times 10^{7} N m^{- 1}$ )

TestHub · Accepted Answer

λ t h = h c e V a 1 λ K α = R z - 1 2 1 1 2 - 1 2 2 13 10 λ K α - λ t h = λ K α - λ t h 2 3 10 λ K α = 13 10 - 1 2 λ t h 3 10 4 × 10 - 7 3 Z - 1 2 = 8 10 12.4 × 10 - 7 15.5 × 10 3 ⇒ 5000 8 = Z - 1 2 625 = Z - 1 2 ⇒ Z = 26

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