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JEE Main 2018 (16 Apr, Shift 1) · Radioactive Decays: Alpha, Beta, Gamma

Radioactive Decays: Alpha, Beta, Gamma question from JEE Main 2018 (16 Apr, Shift 1)

Q24JEE Main 2018 · 16 APR · SHIFT 1Medium

Radioactive Decays: Alpha, Beta, Gamma

Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths λN, λA\lambda_N,\ \lambda_A respectively. The ratio λNλA\frac{\lambda_N}{\lambda_A} is closest to:

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Answer: (a)

  1. Nuclear excitation energies are of order MeV (∼106\sim 10^6 eV); atomic excitation energies are of order eV.
  2. λ=hcE\lambda = \dfrac{hc}{E}, so λNλA=EAEN≈1 eV1 MeV=10−6\dfrac{\lambda_N}{\lambda_A} = \dfrac{E_A}{E_N} \approx \dfrac{1\text{ eV}}{1\text{ MeV}} = 10^{-6}
  3. So the answer is (a) 10−610^{-6}.
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