Radium has a half-life of 1600 years. How many years does it take for 90% of a given amount of radium to decay?
A) $\frac { 1600 } { \ln 5 }$
B) $1600 \ln 2$
C) $\frac { 1600 \ln 10 } { \ln 2 }$
D) $1600 \ln 5$
E) $1600 \ln 10$
F) $\frac { 1600 } { \ln 2 }$
G) $1500 \ln 6$
H) $\frac { 1600 \ln 2 } { \ln 10 }$

Question

Radium has a half-life of 1600 years. How many years does it take for 90% of a given amount of radium to decay?
A) $\frac { 1600 } { \ln 5 }$ 
B) $1600 \ln 2$ 
C) $\frac { 1600 \ln 10 } { \ln 2 }$ 
D) $1600 \ln 5$ 
E) $1600 \ln 10$ 
F) $\frac { 1600 } { \ln 2 }$ 
G) $1500 \ln 6$ 
H) $\frac { 1600 \ln 2 } { \ln 10 }$

Quizplus · Accepted Answer

The formula to calculate the time it takes for a certain percentage of a substance to decay is derived from the half-life formula: $t = \frac{\ln(\frac{1}{remaining\ fraction})}{\ln(2)} \times half\ life$. For 90% decay, the remaining fraction is 0.1 (100% - 90% = 10% remaining). Substituting the values: $t = \frac{\ln(10)}{\ln(2)} \times 1600$, which matches option C.

Radium Has a Half-Life of 1600 Years 1600ln⁡5\frac { 1600 } { \ln 5 }ln51600​

Radium Has a Half-Life of 1600 Years $\frac { 1600 } { \ln 5 }$