contestada

Element X decays radioactively with a half life of 6 minutes. If there are 680 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 276 grams?
y = a(.5)

Respuesta :

[tex]\\ \tt\hookrightarrow A=A_o(0.5)^{t/t/2}[/tex]

  • t/2 is half life
  • A is ammount remains
  • A_o is initial amount

[tex]\\ \tt\hookrightarrow 276=680(0.5)^{t/6}[/tex]

[tex]\\ \tt\hookrightarrow 0.5^{t/6}=0.4[/tex]

[tex]\\ \tt\hookrightarrow log0.5^{t/6}=log_10^0.4[/tex]

[tex]\\ \tt\hookrightarrow t/6 (log5-1)=-0.4[/tex]

[tex]\\ \tt\hookrightarrow t/6(0.7-1)=-0.4[/tex]

[tex]\\ \tt\hookrightarrow -0.3(t/6)=-0.4[/tex]

[tex]\\ \tt\hookrightarrow 0.3t/6=0.4[/tex]

[tex]\\ \tt\hookrightarrow t/20=0.4[/tex]

[tex]\\ \tt\hookrightarrow t=8min[/tex]

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