Which is the correct expression for half-life | vedclass

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(D) The decay constant $\lambda$ is related to the half-life $T_{1/2}$ by the equation $N(t) = N_0 e^{-\lambda t}$.At $t = T_{1/2}$,$N(t) = N_0 / 2$.S

Vedclass · Accepted Answer

$(t)_{1/2} = \frac{2.303 \log 2}{\lambda}$

Vedclass · Answer

(D) The decay constant $\lambda$ is related to the half-life $T_{1/2}$ by the equation $N(t) = N_0 e^{-\lambda t}$.At $t = T_{1/2}$,$N(t) = N_0 / 2$.Substituting this,we get $N_0 / 2 = N_0 e^{-\lambda T_{1/2}}$,which simplifies to $1/2 = e^{-\lambda T_{1/2}}$.Taking the natural logarithm on both sides,$\ln(1/2) = -\lambda T_{1/2}$,or $-\ln 2 = -\lambda T_{1/2}$.Thus,$T_{1/2} = \frac{\ln 2}{\lambda}$.Since $\ln 2 = 2.303 \log_{10} 2$,the expression becomes $T_{1/2} = \frac{2.303 \log_{10} 2}{\lambda}$.

Which is the correct expression for half-life?

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