Roboguru

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: dengan  adalah konstanta Rydberg untuk litium dan s dan p adalah konstanta dengan .

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:

begin mathsize 14px style 1 over lambda equals R open parentheses 1 over open parentheses 1 plus s close parentheses squared minus 1 over open parentheses n plus p close parentheses squared close parentheses space space n equals 2 comma 3 comma 4 comma... end style

dengan begin mathsize 14px style R equals 1 comma 09728 cross times 10 to the power of 7 space straight m to the power of negative 1 end exponent end style adalah konstanta Rydberg untuk litium dan s dan p adalah konstanta dengan begin mathsize 14px style p equals negative 0 comma 040 space dan space s equals 0 comma 59 end style.undefined

Pembahasan Soal:

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  undefinedundefined

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 13 Maret 2021

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