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Atoms and Nuclei question

2023 · 25 Jan · Shift 2 · Q65
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Atoms and Nuclei question

2023 · 25 Jan · Shift 2 · Q65

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1
The energy levels of an atom is shown in figure. JEE Main 2023 (Online) 25th January Evening Shift Physics - Atoms and Nuclei Question 90 English Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm? Given (h = 6.62 ×\times× 10 −34^{-34}−34 Js)
  1. A
    C
  2. B
    B
  3. C
    A
  4. D
    D
View written solutionFree

Correct answer: D

  1. Use the photon energy–wavelength relation

For an emitted photon, E=hcλE = \frac{hc}{\lambda}E=λhc​

Given:

  • h=6.62×10−34 J sh = 6.62 \times 10^{-34}\,\text{J s}h=6.62×10−34J s
  • c=3×108 m/sc = 3 \times 10^8\,\text{m/s}c=3×108m/s
  • λ=124.1 nm=124.1×10−9 m\lambda = 124.1\,\text{nm} = 124.1 \times 10^{-9}\,\text{m}λ=124.1nm=124.1×10−9m

So, E=(6.62×10−34)(3×108)124.1×10−9E = \frac{(6.62 \times 10^{-34})(3 \times 10^8)}{124.1 \times 10^{-9}}E=124.1×10−9(6.62×10−34)(3×108)​

E≈19.86×10−26124.1×10−9E \approx \frac{19.86 \times 10^{-26}}{124.1 \times 10^{-9}}E≈124.1×10−919.86×10−26​

E≈1.60×10−18 JE \approx 1.60 \times 10^{-18}\,\text{J}E≈1.60×10−18J

  1. Convert this energy into eV

Using 1 eV=1.6×10−19 J1\,\text{eV} = 1.6 \times 10^{-19}\,\text{J}1eV=1.6×10−19J,

E=1.60×10−181.6×10−19≈10 eVE = \frac{1.60 \times 10^{-18}}{1.6 \times 10^{-19}} \approx 10\,\text{eV}E=1.6×10−191.60×10−18​≈10eV

So the required transition must have energy difference ΔE=10 eV\Delta E = 10\,\text{eV}ΔE=10eV

  1. Match with the energy-level diagram

The transition that gives emission of a photon must be a downward transition whose energy gap is 10 eV10\,\text{eV}10eV.

From the given figure, the transition labeled D corresponds to an energy difference of 10 eV10\,\text{eV}10eV.

Therefore, the correct option is: D\boxed{\text{D}}D​

  1. Compare with stored answer

Stored correct answer: D

My derived answer: D

Hence, they agree.

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