Question

If
$\binom{13}{7}$
N has a half-life of about 10.0 min, how long will it take for 20 g of the isotope to decay to 1.9 g? [2 marks] 2. Radon-22​

Answer 1

Answer:

the time it will take the element to decay to 1.9 g is 34.8 mins.

Explanation:

Given;

half life of Nitrogen, t = 10 min

initial mass of the element, N₀ = 20 g

final mass of the element, N = 1.9 g

The time taken for the element to decay to final mass is calculated as follows;

time (min)                        mass remaining

0 ----------------------------------20 g

10 mins ------------------------- 10 g

20 mins ------------------------- 5 g

30 mins -------------------------- 2.5 g

40 mins --------------------------- 1.25 g

Interpolate between 2.5 g and 1.25 to obtain the time for 1.9 g

30 min ------------------------- 2.5 g

x ----------------------------------- 1.9 g

40 min -------------------------- 1.25 g

$\frac{30 - x}{40- 30} = \frac{2.5 - 1.9}{1.25 - 2.5} \\\\-1.25(30-x) = 6\\\\-37.5 + 1.25x = 6\\\\1.25x = 6+37.5\\\\1.25x = 43.5\\\\x = \frac{43.5}{1.25} \\\\x = 34.8 \ mins$

Therefore, the time it will take the element to decay to 1.9 g is 34.8 mins.