Question

An isotope of sodium, 24Na, has a half-life of 15 hours. A sample of this isotope has mass 9 g. (a) Find the amount remaining after 60 hours. 0.888 X 9 (b) Find the amount remaining after thours. y = (c) Estimate the amount remaining after 4 days. (Round your answer to three decimal places.) 9 (d) Use a graph to estimate the time required for the mass to be reduced to 0.01 g. (Round your answer to one decimal place.) hr

Answer 1

life of Sodium is howes. ag Sample of isotope has mans Amount remaining after 60 hours. the. amount fiest we will estimate and then. Substitute t yeals remaining after t=60 in that Given mos= a grams life meant Haly that half of any cuantity in 15 houts disintegrate with 24 Na 1 (2) mco)= a geams mcis)- Ź (2) - Ostis) m(30) = ₂ ( 2 (2)] : mcus) [zi (30115) £ ces (2) (45115) There fore. His 2. (2) = mct) = 2 -(₂) (tlis) (115) 2 Amount remaining after thouses +115 2 m mct) =

Amount remaining after m (60) = 2(2) remaining after 60 hores. 2x)" 2 16 0.125g. 8 Amount remaining after 60 hours in 8.1259 Amount remaining after 4 days 4 days day = - 24 her 4 days 4x24 heus 96 has 96 ma 2 (₂) 6.4. - 2( ) 2x0.01184 = 0.0236 4 days = 0.0236 grame Amount remaing after (d) 0.019. 비 15 2 C Ź) Oo 비 15 orol = (2) 5x10" (2) 15

0.005= o this (²) of f(x) = g(x) then In (f(x)) = ln (964)) 디 i5 In [G) In Co.oos) toga Cab) bologa ca) tlis inl (Ź) + Is In (₂) In (0.005) 1 2 Inch) - t- - 15 ln (0.005) In (2) t= 114.657