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Berapakah kecepatan dan momentum sebuah proton (m0 = 1,67×10−27 kg) jika dipercepat oleh beda potensial sebesar 2.000 MV?

Pertanyaan

Berapakah kecepatan dan momentum sebuah proton (m0 = begin mathsize 14px style 1 comma 67 cross times 10 to the power of negative 27 end exponent end style kg) jika dipercepat oleh beda potensial sebesar 2.000 MV?undefined 

Pembahasan:

Diketahui:

V equals 2000 space MV equals 2 cross times 10 to the power of 9 space straight V m subscript 0 equals 1 comma 67 cross times 10 to the power of negative 27 end exponent space kg e equals 1 comma 6 cross times 10 to the power of negative 19 end exponent space straight C 

Ditanyakan:

Kecepatan dan momentum proton?

Pembahasan:

Menggunakan persamaan energi relativistik;

table attributes columnalign right center left columnspacing 0px end attributes row cell E K end cell equals cell E minus E subscript 0 end cell row cell e V end cell equals cell fraction numerator m subscript 0 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 0 c squared end cell row cell e V end cell equals cell m subscript 0 c squared open parentheses fraction numerator 1 over denominator square root of 1 minus v squared over c squared end root end fraction minus 1 close parentheses end cell row cell 1 comma 6 cross times 10 to the power of negative 19 end exponent open parentheses 2 cross times 10 to the power of 9 close parentheses end cell equals cell 1 comma 67 cross times 10 to the power of negative 27 end exponent open parentheses 3 cross times 10 to the power of 8 close parentheses 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 comma 2 cross times 10 to the power of negative 10 end exponent end cell equals cell 15 comma 03 cross times 10 to the power of negative 11 end exponent 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 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 end cell equals cell fraction numerator 3 comma 2 cross times 10 to the power of negative 10 end exponent over denominator 15 comma 03 cross times 10 to the power of negative 11 end exponent end fraction end cell row blank equals cell 2 comma 13 end cell row 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 equals cell 2 comma 13 plus 1 end cell row cell square root of 1 minus v squared over c squared end root end cell equals cell fraction numerator 1 over denominator 3 comma 13 end fraction end cell row cell 1 minus v squared over c squared end cell equals cell open parentheses fraction numerator 1 over denominator 3 comma 13 end fraction close parentheses squared end cell row cell v squared over c squared end cell equals cell 1 minus open parentheses fraction numerator 1 over denominator 9 comma 8 end fraction close parentheses end cell row cell v squared over c squared end cell equals cell 0 comma 89 end cell row cell v squared end cell equals cell 0 comma 89 space c squared end cell row v equals cell square root of 0 comma 89 space c squared end root end cell row blank equals cell 0 comma 943 space c end cell end table 

Momentum relativistik proton;

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 open parentheses 1 comma 67 cross times 10 to the power of negative 27 end exponent close parentheses open parentheses 0 comma 943 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 943 space c close parentheses squared over c squared end style end root end fraction end cell row blank equals cell fraction numerator 4 comma 72 cross times 10 to the power of negative 19 end exponent over denominator square root of 1 minus 0 comma 89 end root end fraction end cell row blank equals cell fraction numerator 4 comma 72 cross times 10 to the power of negative 19 end exponent over denominator 0 comma 33 end fraction end cell row blank equals cell 1 comma 43 cross times 10 to the power of negative 18 end exponent space kg space straight m divided by straight s end cell end table 

Dengan demikian, kecepatan proton adalah 0,943c dan momentum relativistik proron 1,43 x 10-18 kg m/s.

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Terakhir diupdate 07 Oktober 2021

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