Answered: X rays are generated by accelerating…

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Question

a. A dental x-ray machine has a 60 kV accelerating voltage and a tungsten target. A
typical exposure uses an 8.0 mA electron current for 18 s. What is the approximate
power of the x-ray emission? The conversion efficiency is not known precisely, so a
one-significant-figure answer is appropriate.

b. What is the x-ray intensity at the jaw, 15 cm from the source? Assume that the x rays
are emitted uniformly in all directions from a single point.

c. A molar tooth can be approximated as a 9-mm-diameter, 20-mm-long cylinder. X rays
impinge on a molar from the side, perpendicular to the axis of the cylinder. Approxi-
mately what x-ray energy enters a molar during the exposure?

4. X rays are generated by accelerating electrons through a large potential difference AV and
allowing them to strike a metal target. Most of the electron energy is dissipated as heat,
but the interaction of the high-speed electrons with the target atoms transforms some of the
energy into x rays. The efficiency of the conversion is approximately (Z x 10-9 V-¹)AV,
where Z is the atomic number of the target.

Expert Solution

Step 1

$\begin{array}{l} G i v e n : \\ t a r g e t u s e d i s t u n g s t e n, h e n c e i t s a t o m i c n u m b e r, Z = 74 \\ t h e p o t e n t i a l d i f f e r e n c e, Δ V = 60 k V = 60 \times 10^{3} V \\ e x p o s u r e c u r r e n t, I = 8.0 m A = 8 \times 10^{- 3} A \\ e x p o s u r e t i m e, t_{e} = 18 s \\ d i s t a n c e b e t w e e n t h e s o u r c e a n d j a w, r = 15 c m = 0.15 m \\ a s s u m e d t h a t s o u r c e i s a p o i n t s o u r c e . \\ d i m e n s i o n o f t h e m o l a r t o o t h, m o d e l l e d a s a c y l i n d e r, \\ l e n g t h o f t h e c y l i n d e r, L = 20 m m = 20 \times 10^{- 3} m \\ d i a m e t e r o f t h e c y l i n d e r, D = 9 \times 10^{- 3} m \\ A s k e d : \\ a . P o w e r o f X - r a y e m m i s s i o n, P_{e} = ? \\ b . I n t e n s i t y o f t h e r a d i a t i o n s a t t h e j a w, I = ? \\ c . A m o u n t o f e n e r g y t h a t e n t e r s t h e m o l a r t o o t h \\ d u r i n g t h e e x p o s u r e t i m e, E = ? \end{array}$

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