If the half-life of a radioactive isotope is 5000 years, then its decay constant is

A) $- \frac { 2 } { \ln 5000 }$
B) $- \frac { 1 } { \ln 2500 }$
C) $- \frac { \ln 2 } { \ln 5000 }$
D) $- \frac { \ln 2 } { 5000 }$
E) $- \frac { \ln 5000 } { 2 }$

Question

If the half-life of a radioactive isotope is 5000 years, then its decay constant is

A) $- \frac { 2 } { \ln 5000 }$
B) $- \frac { 1 } { \ln 2500 }$
C) $- \frac { \ln 2 } { \ln 5000 }$
D) $- \frac { \ln 2 } { 5000 }$
E) $- \frac { \ln 5000 } { 2 }$

Quizplus · Accepted Answer

The decay constant ($\lambda$) is related to the half-life ($T_{1/2}$) of a radioactive isotope by the formula $\lambda = \frac{\ln 2}{T_{1/2}}$. Substituting $T_{1/2} = 5000$ years into this formula gives $\lambda = -\frac{\ln 2}{5000}$, which matches option D.

If the Half-Life of a Radioactive Isotope Is 5000 Years −2ln⁡5000- \frac { 2 } { \ln 5000 }−ln50002​

If the Half-Life of a Radioactive Isotope Is 5000 Years $- \frac { 2 } { \ln 5000 }$