The isotope chromium-51 has a half-life of 28 days. If the original sample had a mass of 28.0 grams, what mass of the chromium-51 sample remains after 84 days?

Md Ariful Islam

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Md Ariful Islam

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To find the mass of the chronium-51 sample that remains after $84$ days, we can use the half-life formula.

Recall the half-life formula:

$color(blue)(|bar(ul(color(white)(a/a)A=A_0(1/2)^(t/h)color(white)(a/a)|)))$

where:
$A=$final amount
$A_0=$initial amount
$t=$time elapsed
$h=$time for half of initial amount to remain after decay (also known as half-life)

Plugging in our known values,

$A=28.0g(1/2)^((84color(white)(i)"days")/(28color(white)(i)"days"))$

$A=color(green)(|bar(ul(color(white)(a/a)color(black)(3.50g)color(white)(a/a)|)))$

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