Question

Can someone help me with this Physics question please?

Q. The half-life of tritium (hydrogen-3) is 12.3 years. If 48.0mg of tritium is released from a nuclear power plant during the course of a mishap, what mass of the sample will remain after 49.2 years?​

Answer 1

Step-by-step explanation:

The formula for this, the easy one, is

`N=N_0((1)/(2))^{(t)/(H)` where No is the initial amount of the element, t is the time in years, and H is the half life. Filling in:

`N=48.0((1)/(2))^{(49.2)/(12.3)` and simplifying a bit:

`N=48.0(.5)^4` and

N = 48.0(.0625) so

N = 3 mg left after 12.3 years

Answer 2

How many half-lifes is 49.2 years ?

(49.2 years) / (12.3 years per half-life) = 4 half-lifes.

In 4 half-lifes, (1/2) · (1/2) · (1/2) · (1/2) of the original sample remains.

That's (1/2⁴) or (1/16) of the original.

(1/16) of 48.0 mg = 3 mg .

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Step-by-step:

== Start with 48 mg .

== After one half-life, 24 mg remains.

== Then, after the second half-life, 12 mg remains.

== Then, after the third half-life, 6 mg remains.

== Then, after the fourth half-life, 3 mg remains.