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JEE Main 201911 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Morning Shift
Subject
Physics
Chapter
Atomic Physics

JEE Main 2019 · 11 January · Morning Shift · Physics · Atomic Physics

A hydrogen atom, initially in the ground state is excited by...

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980A~…980 Ã…. The radius of the atom in the excited state, in terms of Bohr radius a0a_{0}, will be:

Options

  1. A25a025 \mathrm{a}_{0}
  2. B9a09 a_{0}
  3. C16a016 \mathrm{a}_{0}
  4. DNone of the above

Correct answer

C. 16a016 \mathrm{a}_{0}

Step-by-step solution

Energy of photon =hcλ=12500980=12.75eV=\frac{\mathrm{hc}}{\lambda}=\frac{12500}{980}=12.75 \mathrm{eV} Energy of electron in nth \mathrm{n}^{\text{th }} orbit is given by En=−13.6n2⇒En−E1=−13.6[1n2−112]⇒12.75=13.6[112−1n2]⇒n=4∴\mathrm{En}=\frac{-13.6}{\mathrm{n}^{2}} \Rightarrow \mathrm{E}_{\mathrm{n}}-\mathrm{E}_{1}=-13.6\left[\frac{1}{\mathrm{n}^{2}} \frac{-1}{1^{2}}\right] \Rightarrow 12.75=13.6\left[\frac{1}{1^{2}} \frac{-1}{\mathrm{n}^{2}}\right] \Rightarrow \mathrm{n}=4 \therefore Electron will excite to n=4\mathrm{n}=4 We know that ' R′∝n2∴R^{\prime} \propto n^{2} \therefore Radius of atom will be 16a016 \mathrm{a}_{0}
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