The radioisotope, tritium 13(H) has a half-life of 12.3 years. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 years:

Question

In 2-chloro-3,4-dimethylhexane, how many chiral carbon atoms are present?

Answer 1

To determine how much tritium remains after 49.2 years, we need to use the concept of radioactive decay and half-life. The half-life of tritium \((^3_1H)\) is the time required for half of the radioactive nuclei to decay.

The formula to calculate the remaining amount of a radioisotope after a certain period is given by:

N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}

where:

N = remaining amount of the isotope
N_0 = initial amount of the isotope (32 mg in this case)
t = time elapsed (49.2 years)
t_{1/2} = half-life of the isotope (12.3 years)

Substituting the given values into the formula, we have:

N = 32 \left(\frac{1}{2}\right)^{\frac{49.2}{12.3}}

Calculate the exponent:

\frac{49.2}{12.3} = 4

Thus, the formula becomes:

N = 32 \left(\frac{1}{2}\right)^{4}

Calculate the power of the half:

N = 32 \times \frac{1}{16}

Therefore, N = 2 \, \text{mg}.

After 49.2 years, 2 mg of the initial 32 mg of tritium will remain.

Answer 2