Question

The cut off wavelength of continuous X-ray from two Coolidge tubes operating at 30 kV but using different target materials (molybdenum Z= 42 and tungsten Z = 74) are

• A. $1\stackrel{\circ }{A},3\stackrel{\circ }{A}$
• B. $0.3\stackrel{\circ }{A},0.2\stackrel{\circ }{A}$
• C. $0.414\stackrel{\circ }{A},0.8\stackrel{\circ }{A}$
• D. $0.414\stackrel{\circ }{A},0.414\stackrel{\circ }{A}$

Answer 1

The correct option is D $0.414\stackrel{\circ }{A},0.414\stackrel{\circ }{A}$

Cut off wavelength of continuous X-rays depends solely on the voltage applied and does not depend on the material of the target. Hence the two tubes will have the same cut off wavelength.
$Ve=hv=\frac{hc}{\lambda }or\lambda =\frac{hc}{Ve}=\frac{6.627\times {10}^{-34}\times 3\times {10}^8}{30\times {10}^3\times 1.6\times {10}^{-19}}m=0.414\times {10}^{-10}m=0.414\stackrel{\circ }{A}$.