calculating half life. (physics question)?

Question

after 2.00 days, the activity of a sample of an unknown type of radioactive material has decreased to 84.2% of the initial activity. What is the half life of this material.

Answer 1

Step 1: determine τ:
Q = Qo exp(−t/τ)
Q/Qo = exp(−t/τ)
t/τ = ln Qo/Q
τ = t / ln Qo/Q = 2 / ln 0.842^-1 = 11.6296 d

Step 2: determine t_½:
Q/Qo = ½ = exp(−t_½/τ)
exp(t_½/τ) = 2
t_½ = τ ln 2 = 11.6296 ln 2 = 8.061 d

Answer 2

The 0.5-existence is while 0.5 of the atoms have decayed. consequently the cpm would be 0.5 as plenty. you're able to initiate at 6100cpm. in simple terms draw a line throughout the time of while the cpm is 0.5 of 6100 (3050) and then draw yet another line down from the factor the place the 1st line touches the curved line. The time taken to take action factor will then be the place the vertical line touches the x (time) axis. it is the 0.5 existence.

Answer 3

t sub 1/2 = In(2) /λ

* ln(2) is the natural logarithm of 2 (approximately 0.693), and
* λ is the decay constant, a positive constant used to describe the rate of exponential decay.

Answer 4

.842 = (1/2)^(2days/t)
ln(.842)=(2days/t)ln(1/2)
t = 2days(ln(1/2))/ln(.842) = 8.06days