= 6.25 g
Half life is the time taken for a radioactive material to decay by half of its original amount.
To calculate the new amount of a radioactive substance we use;
New amount = Original amount × (1/2)^n, where n is the number of half lives.
Therefore;
n = 20.25/6.75
= 3
Thus; New amount = 50 × (1/2)³
= 50 × 1/8
= 6.25 g
The sample of the pa-234 that remains will be 6.25 g
Answer:
The parent isotope remain after 20.25 hours will be 6.25 grams.
Explanation:
Initial mass of the Pa-234 isotope = 50.0 g
Time taken by the sample, t = 20.25 hr
Formula used :
[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
where,
[tex]N_o[/tex] = initial mass of isotope
N = mass of the parent isotope left after the time, (t)
[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope = 6.75 hr
[tex]\lambda[/tex] = rate constant
Now put all the given values in this formula, we get
[tex]N=50.0 g\times e^{-(\frac{0.693}{6.75 hr})\times 20.25 hr}[/tex]
[tex]N=6.253 g[/tex]
Therefore, the parent isotope remain after 20.25 hours will be 6.25 grams.
