Atoms & Nuclei

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123 of 239

Question 123 of 239

A photon is emitted in transition from n=4ton=1n=4ton=1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h=4×10−15eVsh=4\times {10}^{-15}eVs)

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Answer: (D) 94.1nm94.1nm

Using the relation between energy of photon and wavelength for the transition in the hydrogen atom, we get
hcλ=13.6[1n12−1n22]\dfrac{hc}{\lambda }=13.6\left[\dfrac{1}{{n}_{1}^{2}}-\dfrac{1}{{n}_{2}^{2}}\right]
⇒4×10−15×3×108λ=13.6[1−116]⇒λ=12×10−7×1613.6×15=94.1×10−9=94.1nm\Rightarrow \dfrac{4\times {10}^{-15}\times 3\times {10}^{8}}{\lambda }=13.6\left[1-\dfrac{1}{16}\right] \Rightarrow \lambda =\dfrac{12\times {10}^{-7}\times 16}{13.6\times 15}=94.1\times {10}^{-9}=94.1nm

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