Pertanyaan

Satu dari garis spektral atom litium adalah deret dengan panjang gelombang berikut: 670,79 nm, 323,26 nm, 247,53 nm. Tunjukkan bahwa panjang gelombang ini hampir sesuai dengan rumus: λ 1 = R ( ( 1 + s ) 2 1 − ( n + p ) 2 1 ) n = 2 , 3 , 4 , ... dengan R = 1 , 09728 × 1 0 7 m − 1 adalah konstanta Rydberg untuk litium dan s dan p adalah konstanta dengan p = − 0 , 040 dan s = 0 , 59 .

Satu dari garis spektral atom litium adalah deret dengan panjang gelombang berikut: 670,79 nm, 323,26 nm, 247,53 nm. Tunjukkan bahwa panjang gelombang ini hampir sesuai dengan rumus:

$\frac{1}{λ} = R (\frac{1}{( 1 + s ) ^{2}} - \frac{1}{( n + p ) ^{2}}) n = 2, 3, 4, ...$

dengan $R = 1, 09728 \times 1 0^{7} m^{- 1}$ adalah konstanta Rydberg untuk litium dan s dan p adalah konstanta dengan $p = - 0, 040 dan s = 0, 59$ .

Y. Maghfirah

Master Teacher

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Pembahasan

$begin mathsize 14px style n equals 2 1 over lambda equals R left parenthesis 1 over open parentheses 1 plus s close parentheses squared minus 1 over open parentheses n plus p close parentheses squared right parenthesis 1 over lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis 1 over open parentheses 1 plus 0 comma 59 close parentheses squared minus 1 over open parentheses 2 minus 0 comma 040 close parentheses squared right parenthesis 1 over lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis 1 over open parentheses 1 comma 59 close parentheses squared minus 1 over open parentheses 1 comma 96 close parentheses squared right parenthesis 1 over lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 1 over denominator 2 comma 5281 end fraction minus fraction numerator 1 over denominator 3 comma 8416 end fraction right parenthesis 1 over lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 3 comma 8416 minus 2 comma 5281 over denominator 9 comma 71194896 end fraction right parenthesis 1 over lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 1 comma 3135 over denominator 9 comma 71194896 end fraction right parenthesis 1 over lambda equals 0 comma 1484 cross times 10 to the power of 7 lambda equals fraction numerator 1 over denominator 0 comma 1484 cross times 10 to the power of 7 end fraction equals 6 comma 7385 cross times 10 to the power of negative 7 space end exponent straight m equals 673 comma 85 space nm straight n equals 3 1 over straight lambda equals straight R left parenthesis 1 over open parentheses 1 plus s close parentheses squared minus 1 over open parentheses n plus p close parentheses squared right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis 1 over open parentheses 1 plus 0 comma 59 close parentheses squared minus 1 over open parentheses 3 minus 0 comma 040 close parentheses squared right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 1 over denominator 1 comma 59 squared end fraction minus fraction numerator 1 over denominator 2 comma 96 squared end fraction right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 1 over denominator 2 comma 5281 end fraction minus fraction numerator 1 over denominator 8 comma 7616 end fraction right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 8 comma 7616 minus 2 comma 5281 over denominator 22 comma 15020096 end fraction right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 6 comma 2335 over denominator 22 comma 15020096 end fraction right parenthesis 1 over straight lambda equals 0 comma 3087 cross times 10 to the power of 7 straight lambda equals fraction numerator 1 over denominator 0 comma 3087 cross times 10 to the power of 7 end fraction equals 3 comma 2393 cross times 10 to the power of negative 7 space end exponent straight m equals 323 comma 93 space nm straight n equals 4 1 over straight lambda equals straight R left parenthesis 1 over open parentheses 1 plus straight s close parentheses squared minus 1 over open parentheses straight n plus straight p close parentheses squared right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis 1 over open parentheses 1 plus 0 comma 59 close parentheses squared minus 1 over open parentheses 4 minus 0 comma 040 close parentheses squared right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis 1 over open parentheses 1 comma 59 close parentheses squared minus 1 over open parentheses 3 comma 96 close parentheses squared right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 1 over denominator 2 comma 5281 end fraction minus fraction numerator 1 over denominator 15 comma 6816 end fraction right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 15 comma 6816 minus 2 comma 5281 over denominator 39 comma 64465296 end fraction right parenthesis 1 over straight lambda equals 1 comma 09728 cross times 10 to the power of 7 left parenthesis fraction numerator 13 comma 1535 over denominator 39 comma 64465296 end fraction right parenthesis 1 over straight lambda equals 0 comma 3640 cross times 10 to the power of 7 straight lambda equals fraction numerator 1 over denominator 0 comma 3640 cross times 10 to the power of 7 end fraction equals 2 comma 7472 cross times 10 to the power of negative 7 space end exponent straight m equals 274 comma 72 space nm end style$

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