Question

A certain medical machine emits x-rays with a minimum wavelength of 0.022 nm. One day, the machine has an electrical problem and the voltage applied to the x-ray tube decreases to 80% of its normal value. Now what is the minimum x-ray wavelength produced by the machine? b. What is the maximum x-ray energy this machine (with electrical problems) can produce? c. The atomic number of an element is 82. According to the Bohr model, what is the energy of a Ka x-ray photon?

Answer 1

min = hc / eV

V = hc / emin

V = (6.63 x 10^-34 x 3 x 10^8) / (1.6 x 10^-19 x 0.022 x 10^-9)

V = 56505.68 V

V = 56505.68 V x 0.80 = 45204.55 V

a)

min = hc / eV

min = (6.63 x 10^-34 x 3 x 10^8) / (1.6 x 10^-19 x 45204.55)

min = 2.75 x 10^-11 m

b)

Now min corresponds to a frequency of

f = c / min

f = 3 x 10^8 / 2.75 x 10^-11

f = 1.1 x 10^19 Hz

E = hf

E =  6.63 x 10^-34 x 1.1 x 10^19

E = 7.23 x 10^-15 J

E = 45204 .55 eV

(c)

The energy will be = (Z-1)^2*(E2 - E1) =  82^2*(-3.4eV - (-13.6eV)) = 6.8585 x 10^4 eV