Superman in some ways is like a living solar battery. He gets his power by radia

Question

Superman in some ways is like a living solar battery. He gets his power by radiation from yellow stars (like our sun). Radioactive kryptonite, his only weakness, interferes with this energy absorption process, causing him severe pain and even death for long enough exposures. He can, however, safely approach pieces of kryptonite that are 0.005 kg or less. If a sample of kryptonite has an initial mass of 1.5 kg, what is the minimum amount of time that Superman would have to wait before safely approaching the sample? Take the half-life of kryptonite to be 1 year.

A) 4.15 yrs. B) 3.33 yrs. C) 8.23 yrs. D) 5.7 yrs. E) None of these.

Explanation / Answer

here ,

initial mass , Mo = 1.5 Kg

final mass , m = 0.005 Kg

half life , t0.5 = 1 year

Now, as m = Mo *(0.5)^(t/t0.5)

0.005 = 1.5 * (0.5)^(t/1)

solving for t

t = 8.23 years

the time taken for the sample to be safe is C) 8.23 years

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