Question

How much sample will remain after 40 days for as 200 g sample of Radon-222? The half-life of Radon-222 is 4 days.

Answer 1

Answer:

$\boxed{N_t =0.1953125 \: grams}$

Explanation:

Formula:

$N_t = N_0( { \frac{1}{2} })^{ \frac{t}{t_ \frac{1}{2} } }$

Where Nt is the amount of substance remaining after time t,

N0 is the amount of substance at time t = 0,

t is the time at which we have to find out how much substance disintegrated from t = 0 to t = t

& t_1/2 is the half life corresponding radioactive sample.

Given:

N0 = 200g

t= 40 days

t1/2 = 4 days

To find:

Nt =?

Solution:

Substituting given data in above formula,

$N_t = N_0( { \frac{1}{2} })^{ \frac{t}{t_ \frac{1}{2} } } \\ N_t = 200( { \frac{1}{2} })^{ \frac{40}{4 } } \\ N_t = 200 \times 0.0009765625 \\ \boxed{N_t =0.1953125 \: grams}$

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