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PhysicsModern PhysicsAtomic structureEasy2 minPYQ_2020

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The voltage applied to the Coolidge X-ray tube is increased by $25 %$ . As a result, the short wave limit of continuous X-ray spectrum shifts by $Δ λ$ . The initial voltage applied to the tube is

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Solution:

$\frac{1}{2} {mv}^{2}_{\max} = eV = \frac{hc}{λ}$
$\Rightarrow λ = \frac{hc}{eV} \Rightarrow λ_{1} = \frac{hc}{{eV}_{1}}, λ_{2} = \frac{hc}{{eV}_{2}} \Rightarrow λ_{1} - λ_{2} = \frac{hc}{{eV}_{1}} - \frac{hc}{{eV}_{2}}$
$\Rightarrow Δλ = \frac{hc}{e} [\frac{1}{V_{1}} - \frac{4}{5 V_{1}}] = \frac{hc}{{eV}_{1}} \times \frac{1}{5}$
$V = \frac{hc}{5 \cdot eΔλ}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Modern PhysicsSubtopic:Atomic structure

⏱ 2mℹ️ Source: PYQ_2020

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