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Isotop begin mathsize 14px style U presubscript 92 presuperscript 238 end style meluruh dan menghasilkan begin mathsize 14px style Ra presubscript 88 presuperscript 226 end style. Waktu paruh undefined adalah 1.600 tahun. Ditemukan bahwa X gram undefined akan menghasilkan begin mathsize 14px style 1 comma 2 cross times 10 to the power of negative 5 end exponent space gram space Ra presubscript 88 presuperscript 226 end style. Jika waktu paruh undefined adalah begin mathsize 14px style 4 comma 9 cross times 10 to the power of 9 space tahun end style, hitung X

A. Muhaemin

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

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Jawaban

nilai X adalah 38,70 gram.

Pembahasan

Karena isotop Ra-226 yang ada pada soal berasal dari U-238 maka aktivitas kedua inti harus sama,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell lambda subscript U N subscript U end cell equals cell lambda subscript R a end subscript N subscript R a end subscript end cell row cell fraction numerator up diagonal strike 0 comma 693 end strike over denominator open parentheses t subscript begin display style bevelled 1 half end style end subscript close parentheses subscript U end fraction N subscript U end cell equals cell fraction numerator up diagonal strike 0 comma 693 end strike over denominator open parentheses t subscript begin display style bevelled 1 half end style end subscript close parentheses subscript R a end subscript end fraction N subscript R a end subscript end cell row cell N subscript U over open parentheses t subscript bevelled 1 half end subscript close parentheses subscript U end cell equals cell N subscript R a end subscript over open parentheses t subscript bevelled 1 half end subscript close parentheses subscript R a end subscript end cell row cell N subscript U end cell equals cell open parentheses t subscript bevelled 1 half end subscript close parentheses subscript U cross times N subscript R a end subscript over open parentheses t subscript bevelled 1 half end subscript close parentheses subscript R a end subscript end cell row cell open parentheses m over 238 cross times up diagonal strike 6 comma 02 cross times 10 to the power of 23 end strike close parentheses end cell equals cell open parentheses 4 comma 9 cross times 10 to the power of 9 close parentheses cross times fraction numerator open parentheses begin display style fraction numerator 1 comma 2 cross times 10 to the power of negative 5 end exponent over denominator 226 end fraction end style cross times up diagonal strike 6 comma 02 cross times 10 to the power of 23 end strike close parentheses over denominator 1600 end fraction end cell row m equals cell open parentheses 0 comma 1626 close parentheses open parentheses 238 close parentheses end cell row m equals cell 38 comma 70 space gram end cell end table end style

Jadi, nilai X adalah 38,70 gram.

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