Question

The half-life of silicon-32 is 710 years. If 90 grams is present now, how much will be present in 600 years? Round the answer to three decimal
places.

84.88 g
0g
0.257 g
50.102 g

Answer 1

Answer:

option D

Step-by-step explanation:

Given,

half life of silicon-32 = 710 years

Present silicon-32, N₀ = 90 gm

silicon-32 after 600 years,N = ?

$k = \dfrac{-0.693}{t}$

$k = \dfrac{-0.693}{710}$

k = -0.000976

Now,

$N = N_0 e^{kt}$

$N =90\times e^{-0.000976\times 600}$

$N = 50.104\ g$

Hence, the correct answer is option D.

Answer 2

The amount of silicon-32 remaining after 600 years is 50.102 grams

Half life is the time taken for a substance to decay to half of its original amount. It is given by:

$N=N_o(\frac{1}{2} )^\frac{t}{t_\frac{1}{2} } \\\\N\ is\ the\ value\ of\ the\ substance\ after\ t\ year, t_\frac{1}{2} \ is\ the\ half\ life\\and\ N_o\ is\ the \ original\ amount$

Given that half life = 710 years, original amount is 90 g, t = 600 years, hence:

$N=90(\frac{1}{2} )^\frac{600}{710} \\\\N=50.102\ g$

The amount of silicon-32 remaining after 600 years is 50.102 grams

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