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Standard XII

Physics

Fringe Width in YDSE

The figure sh...

Question

The figure shows the intensity-wavelength relations of X-rays coming from two different Coolidge tubes. The solid curve represents the relation for the tube A in which the potential difference between the target and the filament is V_A and the atomic number of the target material is Z_A. These quantities are V_B and Z_B for the other tube. Then,
(a) V_A > V_B, Z_A > Z_B
(b) V_A > V_B, Z_A < Z_B
(c) V_A < V_B, Z_A > Z_B
(d) V_A > V_B, Z_A < Z_B

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Solution

(b) V_A > V_B, Z_A < Z_B

It is clear from the figure that the X-ray of tube A has less cutoff wavelength than the X-ray of tube B.
$∴ λ_{A} < λ_{B}$
Using Moseley's Law,
$Z_{A} < Z_{B}$
$λ \propto \frac{1}{V}$ , where V is the voltage applied in the X-ray tube.
$∴ V_{A} > V_{B}$

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(b) VA > VB, ZA < ZB It is clear from the figure that the X-ray of tube A has less cutoff wavelength than the X-ray of tube B. ∴ λA<λB Using Moseley's Law, ZA<ZB λ∝1V, where V is the voltage applied in the X-ray tube. ∴ VA>VB

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$∴ V_{A} > V_{B}$