Question

The half-life of radium-226 is 1590 years. (a) A sample of radium-226 has a mass of 50 mg. Find a formula for the mass of the sample that remains after t years. (b) Find the mass after 500 years correct to the nearest milligram. (c) When will the mass be reduced to 40 mg

Answer 1

Answer:

Explanation:

a )

m = m₀ $e^{-\lambda t$

m is mass after time t . original mass is m₀ , λ is disintegration constant

λ = .693 / half life

= .693 / 1590

= .0004358

m = m₀ $e^{- 0.0004358 t}$

b )

m = 50 x $e^{-.0004358\times 500}$

= 40.21 mg .

c )

40 = 50 $e^{-.0004358t$

.8 = $e^{-.0004358t$

$e^{.0004358t$ = 1.25

.0004358 t = .22314

t = 512 years .