Question

The half life of pa-234 is 6.75 hr. How much of a 50.0g sample of this isotope remains after 20.25 hr

Answer 1

The parent isotope remain after 20.25 hours will be 6.25 grams.

Step-by-step explanation:

Initial mass of the Pa-234 isotope = 50.0 g

Time taken by the sample, t = 20.25 hr

Formula used :

`N=N_o* e^(-\lambda t)\\\\\lambda =\frac{0.693}{t_{(1)/(2)}}`

where,

`N_o` = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

`t_{(1)/(2)}` = half life of the isotope = 6.75 hr

`\lambda` = rate constant

Now put all the given values in this formula, we get

`N=50.0 g* e^{-((0.693)/(6.75 hr))* 20.25 hr}`

`N=6.253 g`

Therefore, the parent isotope remain after 20.25 hours will be 6.25 grams.

Answer 2

Answer;

= 6.25 g

Explanation;

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