Question

Hydrogen (₁H¹), deuterium (₁H²), singly ionised helium (₂He⁴⁺) and doubly ionised lithium (₃Li⁸)²⁺ all have one electron around the nucleus. Consider an electron transition from n =2 to n=1. If the wavelengths of emitted radiation are λ₁,λ₂,λ₃ andλ₄, respectively for four elements, then approximately which one of the following is correct?

4λ₁=2λ₂=2λ₃ =λ₄

λ₁=2λ₂=2λ₃ =λ₄

λ₁=λ₂=4λ₃ =9λ₄

λ₁=2λ₂=3λ₃ =4λ₄

Solution

λ₁=λ₂=4λ₃ =9λ₄

For hydrogen atom, we get
$1 over straight lambda space equals space Rz squared open parentheses 1 over 1 squared minus 1 over 2 squared close parentheses 1 over straight lambda subscript 1 space equals space straight R space left parenthesis 1 right parenthesis squared open parentheses 3 over 4 close parentheses fraction numerator begin display style 1 end style over denominator begin display style straight lambda subscript 2 end style end fraction space equals space straight R space left parenthesis 1 right parenthesis squared open parentheses fraction numerator begin display style 3 end style over denominator begin display style 4 end style end fraction close parentheses fraction numerator begin display style 1 end style over denominator begin display style straight lambda subscript 3 end style end fraction space equals space straight R space left parenthesis 2 right parenthesis squared open parentheses fraction numerator begin display style 3 end style over denominator begin display style 4 end style end fraction close parentheses fraction numerator begin display style 1 end style over denominator begin display style straight lambda subscript 4 end style end fraction space equals space straight R space left parenthesis 3 right parenthesis squared open parentheses fraction numerator begin display style 3 end style over denominator begin display style 4 end style end fraction close parentheses fraction numerator begin display style 1 end style over denominator begin display style straight lambda subscript 1 end style end fraction space equals space fraction numerator begin display style 1 end style over denominator begin display style 4 straight lambda subscript 3 end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 9 straight lambda subscript 4 end style end fraction space equals fraction numerator begin display style 1 end style over denominator begin display style straight lambda subscript 2 end style end fraction$

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Wave Optics

Some More Questions From Wave Optics Chapter

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

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