What Potential Difference Should Be Applied Across an X-ray Tube to Get X-ray of Wavelength Not Less than 0.10 Nm? What is the Maximum Energy of a Photon of this X-ray in Joule? - Physics

Sum

What potential difference should be applied across an X-ray tube to get X-ray of wavelength not less than 0.10 nm? What is the maximum energy of a photon of this X-ray in joule?

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

Solution

Given :-

Wavelength of the X-ray, λ = 0.10  "nm"

Planck's constant , h = 6.63 xx 10^-34  "J-s"

Speed of light, c = 3 xx 10^8  "m/s"

Minimum wavelength is given by

lambda_min = (hc)/(eV)

⇒ V = (hc)/(elambda_min)

⇒ V = (6.63 xx 10^-34 xx 3 xx 10^8)/(1.6 xx 10^-19 xx 10^-10)

⇒V = 12.43 xx 10^3  "V" = 12.4  "kV"

Maximum energy of the photon (E) is given by

E = (hc)/lambda

⇒ E = (6.63 xx 10^-34 xx 3 xx 10^8)/(10^-10)

⇒ E = 19.89 xx 10^-16

⇒ E = 1.989 xx 10^-15 ≈  2 xx 10^-15  "J"

Is there an error in this question or solution?