In four years, 40% of a radioactive element decays. Find its half-life. Round to one decimal place.

T(Half Life) = 5.42 s

Step-by-step explanation:

Given :

t = 4years

[R]₀(Initial Concentration) = 100(say)

[R](Concentration Left after time t=4yrs) = 100 - 40 = 60

We know that,

k = 2.303 / t (log{[R]₀/[R]})

where k = rate constant

k = 2.303 / t (log[100/60])

k = 2.303 / 4 (log[10] - log[6])

k = 2.303 / 4 (1 - 0.7781)

k = 2.303 / 4 (0.2219)

k = 0.5110 / 4

k = 0.1277          (i)

Now, to find its half life,

We know that,

T(Half Life) = 0.693 / k

T = 0.693 / 0.1277

T = 5.42 years

1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours

just took the test and my answers down below!

step-by-step explanation:

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