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.