\(^{218}PO\) decays initially at a rate of 816 dps. The rate falls to

1.	\(^{218}PO\) decays initially at a rate of 816 dps. The rate falls to 408 dps after 24 min. Calculate the decay constant.
Answer» Given: \((\frac{-dN_0}{dt})\) = 816 dps, \((\frac{-dN}{dt})\) = 408 dps, t = 24 min To find: Decay constant \((\lambda)\) Formula: \(\lambda\) = \(\frac{2.303}t\) log₁₀\((\frac{N_0}N)\) Calculation: \(\lambda\) = \(\frac{2.303}t\) log₁₀\((\frac{N_0}N)\) \(\lambda\) = \(\frac{2.303}{24}\) log₁₀\((\frac{816}{408})\) = 0.0288 = 0.029 min^-1 Decay constant \((\lambda)\) will be 0.029 min^-1

\(^{218}PO\) decays initially at a rate of 816 dps. The rate falls to 408 dps after 24 min. Calculate the decay constant.

Answer»

Given: \((\frac{-dN_0}{dt})\) = 816 dps, \((\frac{-dN}{dt})\) = 408 dps, t = 24 min

To find: Decay constant \((\lambda)\)

Formula: \(\lambda\) = \(\frac{2.303}t\) log₁₀\((\frac{N_0}N)\)

Calculation: \(\lambda\) = \(\frac{2.303}t\) log₁₀\((\frac{N_0}N)\)

\(\lambda\) = \(\frac{2.303}{24}\) log₁₀\((\frac{816}{408})\)

= 0.0288 = 0.029 min^-1

Decay constant \((\lambda)\) will be 0.029 min^-1