Question

Half life of radium is 1620 years how many radium nuclei decay in 5 hours

Answer 1

Missing point in the question :-

how many radium nuclei decay in 5 hours in 5 gm radium.

Atomic weight of radium - 223

λ = ln2 / t(1/2) = ln2 / 1620 (yrs)⁻¹

λ =  ln2 / 1620 x 365 x 24 (hr)⁻¹

N = N0.e^(–λt) .

Here N0 = 5/223 x 6.022 x 10²³

So, N = No.e^(–λ 5)

Decayed particle = No - N = No ( 1- e^(–λ 5))

Substituting λ and No in above equation we get

decayed particles = 3.29 x 10¹⁵