Pertanyaan

Tunjukkan bahwa garis spektral Deret Balmer semua mempunyai frekuensi lebih tinggi dari spektral garis pada deret Paschen. Apakah semua garis spektral deret Paschen lebih tinggi frekuensinya dibandingkan dengan spektral deret Bracket?

Y. Maghfirah

Master Teacher

Jawaban terverifikasi

Jawaban

frekuensi deret Balmer > deret Paschen > deret Bracket.

Pembahasan

Jadi, frekuensi deret Balmer > deret Paschen > deret Bracket.

$begin mathsize 14px style Deret space Balmer 1 over lambda equals R open parentheses 1 over n subscript A squared minus 1 over n subscript B squared close parentheses 1 over lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 1 over 2 squared minus 1 over 3 squared close parentheses 1 over lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 1 fourth minus 1 over 9 close parentheses 1 over lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 5 over 36 close parentheses 1 over lambda equals 0 comma 152 cross times 10 to the power of 7 lambda equals fraction numerator 1 over denominator 0 comma 152 cross times 10 to the power of 7 end fraction equals 6 comma 58 cross times 10 to the power of negative 7 end exponent f equals c over lambda equals fraction numerator 3 cross times 10 to the power of 8 over denominator 6 comma 58 cross times 10 to the power of negative 7 end exponent end fraction equals 0 comma 46 cross times 10 to the power of 15 equals 46 cross times 10 to the power of 13 space Hz Deret space Paschen 1 over straight lambda equals straight R open parentheses 1 over straight n subscript straight A squared minus 1 over straight n subscript straight B squared close parentheses 1 over straight lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 1 over 3 squared minus 1 over 4 squared close parentheses 1 over straight lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 1 over 9 minus 1 over 16 close parentheses 1 over straight lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 7 over 144 close parentheses 1 over straight lambda equals 0 comma 0533 cross times 10 to the power of 7 straight lambda equals fraction numerator 1 over denominator 0 comma 0533 cross times 10 to the power of 7 end fraction equals 18 comma 76 cross times 10 to the power of negative 7 end exponent straight f equals straight c over straight lambda equals fraction numerator 3 cross times 10 to the power of 8 over denominator 18 comma 76 cross times 10 to the power of negative 7 end exponent end fraction equals 0 comma 16 cross times 10 to the power of 15 equals 16 cross times 10 to the power of 13 space Hz Deret space Bracket 1 over straight lambda equals straight R open parentheses 1 over straight n subscript straight A squared minus 1 over straight n subscript straight B squared close parentheses 1 over straight lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 1 over 4 squared minus 1 over 5 squared close parentheses 1 over straight lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 1 over 16 minus 1 over 25 close parentheses 1 over straight lambda equals 1 comma 097 cross times 10 to the power of 7 open parentheses 9 over 400 close parentheses 1 over straight lambda equals 0 comma 0247 cross times 10 to the power of 7 straight lambda equals fraction numerator 1 over denominator 0 comma 0247 cross times 10 to the power of 7 end fraction equals 40 comma 49 cross times 10 to the power of negative 7 end exponent straight f equals straight c over straight lambda equals fraction numerator 3 cross times 10 to the power of 8 over denominator 40 comma 49 cross times 10 to the power of negative 7 end exponent end fraction equals 0 comma 07 cross times 10 to the power of 15 equals 7 cross times 10 to the power of 13 space Hz end style$

Jadi, frekuensi deret Balmer > deret Paschen > deret Bracket.