Pertanyaan

Hitung momentum elektron yang energi kinetiknya 3,0 x 10 -13 J! Massa elektron 9,1 x 10 -31 kg.

Hitung momentum elektron yang energi kinetiknya 3,0 x 10^-13J! Massa elektron 9,1 x 10^-31 kg.

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Jawaban terverifikasi

Jawaban

momentum elektron tersebut bernilai 1,23 x 10 -21 kg m/s.

momentum elektron tersebut bernilai 1,23 x 10^-21 kg m/s.

Pembahasan

Tentukan kecepatan elektron terlebih dahulu dengan menggunakan persamaan energi totalrelatiivistik: Jadi, kecepatan elektron tersebut adalah 0,9761 c, sehingga momentum relativistiknya: Jadi, momentum elektron tersebut bernilai 1,23 x 10 -21 kg m/s.

Tentukan kecepatan elektron terlebih dahulu dengan menggunakan persamaan energi total relatiivistik:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell E subscript k end cell equals cell E minus E subscript o end cell row cell E subscript k end cell equals cell fraction numerator m subscript o c squared over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction minus E subscript o end cell row cell E subscript k end cell equals cell fraction numerator m subscript o c squared over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction minus m subscript o c squared end cell row cell E subscript k end cell equals cell m subscript o c squared open parentheses fraction numerator 1 over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction minus 1 close parentheses end cell row cell 3 cross times 10 to the power of negative 13 end exponent end cell equals cell 9 comma 1 cross times 10 to the power of negative 31 end exponent left parenthesis 3 cross times 10 to the power of 8 right parenthesis squared open parentheses fraction numerator 1 over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction minus 1 close parentheses space end cell row cell fraction numerator 3 cross times 10 to the power of negative 13 end exponent over denominator 8 comma 19 cross times 10 to the power of negative 14 end exponent end fraction end cell equals cell open parentheses fraction numerator 1 over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction minus 1 close parentheses end cell row cell 0 comma 366 cross times 10 to the power of 1 end cell equals cell open parentheses fraction numerator 1 over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction minus 1 close parentheses end cell row blank blank blank row cell 3 comma 6 plus 1 end cell equals cell fraction numerator 1 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 blank blank row cell left parenthesis 4 comma 6 right parenthesis squared end cell equals cell open parentheses fraction numerator 1 over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction close parentheses squared space end cell row cell 21 comma 16 end cell equals cell fraction numerator 1 over denominator 1 minus begin display style v squared over c squared end style end fraction end cell row cell 21 comma 16 open parentheses 1 minus v squared over c squared close parentheses end cell equals 1 row cell 21 comma 16 minus fraction numerator 21 comma 16 v squared over denominator c squared end fraction end cell equals 1 row cell 20 comma 16 end cell equals cell fraction numerator 21 comma 16 v squared over denominator c squared end fraction end cell row cell 21 comma 16 v squared end cell equals cell 20 comma 16 c squared end cell row cell v squared end cell equals cell fraction numerator 20 comma 16 c squared over denominator 21 comma 16 end fraction end cell row cell v squared end cell equals cell 0 comma 9527 c squared end cell row v equals cell 0 comma 9761 c end cell end table end style$

Jadi, kecepatan elektron tersebut adalah 0,9761c, sehingga momentum relativistiknya:

$begin mathsize 14px style p equals m v p equals fraction numerator m subscript o v over denominator square root of 1 minus begin display style v squared over c squared end style end root end fraction p equals fraction numerator 9 comma 1 cross times 10 to the power of negative 31 end exponent 0 comma 9761 c over denominator square root of 1 minus begin display style open parentheses 0 comma 9761 c close parentheses squared over c squared end style end root end fraction p equals fraction numerator 9 comma 1 cross times 10 to the power of negative 31 end exponent 0 comma 9761 times 3 cross times 10 to the power of 8 over denominator square root of 0 comma 0472 end root end fraction p equals fraction numerator 26 comma 65 cross times 10 to the power of negative 23 end exponent over denominator 0 comma 2173 end fraction p equals 122 comma 64 cross times 10 to the power of negative 23 end exponent p equals 1 comma 23 cross times 10 to the power of negative 21 end exponent space kg space straight m divided by straight s end style$

Jadi, momentum elektron tersebut bernilai 1,23 x 10^-21 kg m/s.

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