For the following problems, be sure to use an appropriated formula (i.g half lif

Question

For the following problems, be sure to use an appropriated formula (i.g half life or intergrade law), not any short cuts

Polonium-214 has a relatively short half-life of 164 s. How many seconds would it take for 8.0 g of this isotope to decay to 0.25 g?

The half life of argon is 6.32 days, how much of argon- 35 would be left after 50.56 days when there was initially 126.35 grams.

The radioisotope radon-222 has a half-life of 3.8 days. How much of an initial 20.0-g sample of radon-222 would remain after 15.2 days?

7. The mass of cobalt-60 in a sample is found to have decreased to 0.200 g in a period of 1015.5 years. The half life of cobalt is 425.26 years, what was the initial amount of the sample of cobalt-60?

Explanation / Answer

1)

half -life = t1/2 = 164 s

k = 0.693/ t1/2

    = 0.693 / 164

    = 4.22 x 10^-3 s-1

k = (2.303/t )( log a/a-x )

4.22 x 10^-3 = (2.303 / t)( log 8/0.25 )

     t = 821.4 sec

time taken = 821.4 sec

2) The half life of argon is 6.32 days, how much of argon- 35 would be left after 50.56 days when there was initially 126.35 grams.

half -life = t1/2 = 6.32 days

k = 0.693/ t1/2

    = 0.693 / 6.32

    = 0.1096 day-1

k = (2.303/t )( log a/a-x )

0.1096 = (2.303 / 50.56)( log (126.35/ a-x ))

(126.35/ a-x ) = 254.68

a - x = 0.496

remained = 0.496 g

3)

half -life = t1/2 = 3.8 days

k = 0.693/ t1/2

    = 0.693 / 3.8

    = 0.1823 day-1

k = (2.303/t )( log a/a-x )

0.1823 = (2.303 / 15.2)( log (20.0/ a-x ))

(20.0/ a-x ) = 15.96

a - x = 1.25 g

remained = 1.25 g

4)

The mass of cobalt-60 in a sample is found to have decreased to 0.200 g in a period of 1015.5 years. The half life of cobalt is 425.26 years, what was the initial amount of the sample of cobalt-60?

half -life = t1/2 = 425.26 days

k = 0.693/ t1/2

    = 0.693 / 425.26

    = 1.63 x 10^-3 year -1

k = (2.303/t )( log a/a-x )

1.63 x 10^-3 = (2.303 / 1015.5)( log (a/ 0.2))

(a/ 0.2) = 5.22

a = 1.045 g

initial is 1.045 g

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