# 27. The half-life period of a radioactive element is10 days. Then how long does it take for 90% ofa given mass of this element to disintegrate -(1) 19 days (2) 27 days(3) 33 days (4) 47 days

jitendra
18 Points
6 years ago
27. The half-life period of a radioactive element is
10 days. Then how long does it take for 90% of
a given mass of this element to disintegrate -
(1) 19 days (2) 27 days
(3) 33 days (4) 47 days
Rishabh Ranjan
63 Points
6 years ago
The answer to the above question is (3) 33 days
Firstly, we calculate disintegration constant which is equal to 0.693 divided by half life period of the given element. (Pls take care of the units. Here I am taking the unit of disintegration constant(l) as day-1)
Then we calculate the time taken for the element to disintegrate to just 10% of its original mass (Since (100-90)%=10%).
Now let us take N0=100k and N=10k
Now use the formula t=1/l * ln (100k/10k)
Putting values in the equation, we get
t=1/0.0693 * ln 10 = 14.43 * 2.303 = 33.23, which is approximately equal to 33 days.
Therefore, 90% of a given mass of this element will disintegrate in 33 days (approx.)