Find the wavelength of the short-wave limit of an `X`-ray continuous spectrum if electrons approach the anticathode of the tube with velocity `v = 0.85 c`, where `c` is the velocity of light.

Find the wavelength of the short-wave limit of an `X`-ray continuous s

1.	Find the wavelength of the short-wave limit of an `X`-ray continuous spectrum if electrons approach the anticathode of the tube with velocity `v = 0.85 c`, where `c` is the velocity of light.
Answer» The wavelength of `X`-rays is the least when all the `K.E.` of the electrons approaching the anticathode is converted into the energy of `X-`ray. But the `K.E.` of electron is `T_(m) = mc^(2) [(1)/(sqrt(1-v^(2)//c^(2)))-1]` `(mc^(2) =` rest mass energy of electrons `= 0.511MeV`) Thus `(2pi cancelh c)/(lambda) = T_(m)` or `lambda = (2pi cancelh c)/(T_(m)) = (2pi cancelh)/(mc) [(1)/(sqrt(1-v^(2)//c^(2))-1)]^(-1)` `= (2picancelh)/(mc(gamma-1)), gamma = (1)/(sqrt(1-v^(2)//c^(2))) = 2.70 pm`

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Find the wavelength of the short-wave limit of an `X`-ray continuous spectrum if electrons approach the anticathode of the tube with velocity `v = 0.85 c`, where `c` is the velocity of light.

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