The intensity distribution of X-rays from two Coolidge tubes operated on different voltages V1 and V2 and using different target materials of atomic numbers Z1 and Z2 is shown in the figure. Which one of the following inequalities is true?

(see graph) ⇒ V1 > V2 Moseley’s law ⇒ λ1 > λ2 (see graph for characteristic lines) ⇒ . Z2 > Z1.

The intensity distribution of X-rays from two Coolidge tubes operated on different voltages V1 and V2 and using different target materials of atomic numbers Z1 and Z2 is shown in the figure. Which one of the following inequalities is true?

(see graph) ⇒ V1 > V2 Moseley’s law ⇒ λ1 > λ2 (see graph for characteristic lines) ⇒ . Z2 > Z1.

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The intensity distribution of X-rays from two Coolidge tubes operated on different voltages V₁and V₂ and using different target materials of atomic numbers Z₁ and Z₂is shown in the figure. Which one of the following inequalities is true?

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V1 = V2, Z1 < Z2

V₁ > V₂, Z₁ < Z₂

V₁ < V₂, Z₁ > Z₂

V₁ > V₂, Z₁ > Z₂

answer is A.

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Detailed Solution

${\lambda _{\min }} = \frac{{hc}}{{eV}}\, \Rightarrow \,\lambda \propto \frac{1}{V}$
$\because \;{\lambda _2} > {\lambda _1}\,$ (see graph) ⇒ V₁ > V₂Moseley’s law
$\nu \propto {(Z - 1)^2}\,$ ⇒ $\lambda \propto \frac{1}{{{{(Z - 1)}^2}}}$ $\left( {\because \;\nu \propto \frac{1}{\lambda }} \right)$
λ₁ > λ₂ (see graph for characteristic lines) ⇒ . Z₂ > Z₁.