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Pertanyaan

Gunakan perhitungan relativistik untuk menghitung panjang gelombang de Broglie dari sebuah proton yang bergerak dengan kecepatan begin mathsize 14px style 0 comma 6 space c end style!

R. Anjasmara

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

panjang gelombang proton tersebut adalah begin mathsize 14px style 1 comma 76 cross times 10 to the power of negative 15 end exponent space straight m end style.

Pembahasan

Dengan data diberikan;

begin mathsize 14px style h equals 6 comma 626 cross times 10 to the power of negative 34 end exponent space straight J. straight s m subscript p r o t o n end subscript equals 1 comma 67 cross times 10 to the power of negative 27 end exponent space kg c equals 3 cross times 10 to the power of 8 space straight m divided by straight s v equals 0 comma 6 space c end style 

Momentum proton dihitung menggunakan persamaan momentum relativistik;

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row p equals cell m v end cell row blank equals cell fraction numerator m subscript 0 v over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator 1 comma 67 cross times 10 to the power of negative 27 end exponent open parentheses 0 comma 6 cross times 3 cross times 10 to the power of 8 close parentheses over denominator square root of 1 minus begin display style open parentheses 0 comma 6 c close parentheses squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator 3 comma 006 cross times 10 to the power of negative 19 end exponent over denominator square root of 1 minus 0 comma 36 end root end fraction end cell row blank equals cell 3 comma 7575 cross times 10 to the power of negative 19 end exponent space kg. straight m divided by straight s end cell end table end style 

Panjang gelombang menggunakan persamaan de Broglie;

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row lambda equals cell h over p end cell row blank equals cell fraction numerator 6 comma 626 cross times 10 to the power of negative 34 end exponent over denominator 3 comma 7575 cross times 10 to the power of negative 19 end exponent end fraction end cell row blank equals cell 1 comma 76 cross times 10 to the power of negative 15 end exponent space straight m end cell end table end style 

Dengan demikian, panjang gelombang proton tersebut adalah begin mathsize 14px style 1 comma 76 cross times 10 to the power of negative 15 end exponent space straight m end style.

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