Notes: Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?

Thursday, 26 March 2015

Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?

Formula: $\displaystyle{y}={C}{{e}}^{{{k}{t}}}$ where y is the amount of radioactive radium at time t, k is the decay constant, and C is the initial amount of radium

$\displaystyle\frac{{1}}{{2}}{C}={C}{{e}}^{{{k}\cdot{1599}}}$

$\displaystyle\frac{{1}}{{2}}={{e}}^{{{k}\cdot{1599}}}$

$\displaystyle{\ln{{\left(\frac{{1}}{{2}}\right)}}}={1599}{k}{\ln{{e}}}$

$\displaystyle{\ln{{\left(\frac{{1}}{{2}}\right)}}}={1599}{k}$

$\displaystyle\frac{{\ln{{\left(\frac{{1}}{{2}}\right)}}}}{{1599}}={k}$

$\displaystyle{k}=-{4.3349}{x}{{10}}^{{-{{4}}}}$

$\displaystyle{y}={C}{{e}}^{{{k}{t}}}$

$\displaystyle{y}={C}{{e}}^{{{\left(-{4.3349}{x}{{10}}^{{-{{4}}}}\right)}{\left({100}\right)}}}$

$\displaystyle{y}={.9576}{C}$

Final Answer: 95.76% of radioactive radium is left after 100 years.

Formula: $\displaystyle{y}={C}{{e}}^{{{k}{t}}}$ where y is the amount of radioactive radium at time t, k is the decay constant, and C is the initial amount of radium

$\displaystyle\frac{{1}}{{2}}{C}={C}{{e}}^{{{k}\cdot{1599}}}$

$\displaystyle\frac{{1}}{{2}}={{e}}^{{{k}\cdot{1599}}}$

$\displaystyle{\ln{{\left(\frac{{1}}{{2}}\right)}}}={1599}{k}{\ln{{e}}}$

$\displaystyle{\ln{{\left(\frac{{1}}{{2}}\right)}}}={1599}{k}$

$\displaystyle\frac{{\ln{{\left(\frac{{1}}{{2}}\right)}}}}{{1599}}={k}$

$\displaystyle{k}=-{4.3349}{x}{{10}}^{{-{{4}}}}$

$\displaystyle{y}={C}{{e}}^{{{k}{t}}}$

$\displaystyle{y}={C}{{e}}^{{{\left(-{4.3349}{x}{{10}}^{{-{{4}}}}\right)}{\left({100}\right)}}}$

$\displaystyle{y}={.9576}{C}$

Final Answer: 95.76% of radioactive radium is left after 100 years.

Notes

Thursday, 26 March 2015

Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?

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How are race, gender, and class addressed in Oliver Optic's Rich and Humble?

Thursday, 26 March 2015

Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?

No comments:

Post a Comment

How are race, gender, and class addressed in Oliver Optic&#39;s Rich and Humble?

How are race, gender, and class addressed in Oliver Optic's Rich and Humble?