Hi
Radioactive decay -
A radioactive nuclide has a decay constant of - 10^-6 s-1 what is its half life ?
I have come up with
is IN (2) / 0.000001 s-1 = 693147.18055
which i am having troube working into real figures
Can anyone help please .. thanks
.5=e^-kt=e^-1E-6t
thalfffffffffffff=-ln.5/1E-6
I agree with that answer, 693 thousand seconds, or about 8 days. Work it out exactly.
Thank you for your time ..
Sure! I can help you with that.
The decay constant (λ) is the probability of a radioactive nuclide decaying per unit of time. In this case, the decay constant is -10^-6 s^-1.
The half-life (t₁/₂) is the time it takes for half of the radioactive nuclide to decay. To find the half-life, you can use the following equation:
t₁/₂ = ln(2) / λ
Let's plug in the given value of λ:
t₁/₂ = ln(2) / (-10^-6 s^-1)
To convert the negative exponent into a positive exponent, we can rewrite the decay constant as 10^6 s^-1. Now we have:
t₁/₂ = ln(2) / (10^6 s^-1)
Using a calculator, the natural logarithm of 2 (ln(2)) is approximately 0.693. So:
t₁/₂ ≈ 0.693 / (10^6 s^-1)
To simplify the units, we can rewrite 10^6 s^-1 as 10^6 s / s. Now we have:
t₁/₂ ≈ 0.693 / (10^6 s / s)
When we divide by a fraction, we can multiply by the reciprocal of that fraction. In this case, multiplying by the reciprocal of 10^6 s / s (which is 1 s / 10^6 s) gives us:
t₁/₂ ≈ 0.693 * (1 s / 10^6 s)
We can cancel out the unit of seconds (s) and multiply the numbers:
t₁/₂ ≈ 0.693 * 10^-6
Calculating this expression, we find:
t₁/₂ ≈ 6.93 * 10^-7 seconds
So, the half-life of the radioactive nuclide is approximately 6.93 * 10^-7 seconds.
I hope this helps! Let me know if you have any further questions.