Question

Element A has a half-life of 10 days. A scientist measures out 200 g of this substance. After 30 days has passed, the scientist reexamines the sample.
How much Element A will remain in the sample?

50 g
25 g
12.5 g
100 g

Answer 1

Answer:

25 g of an element will remain in  the sample.

Explanation:

Initial mass of an element = $N_o = 200 g$

Final mass of an elemnt after time ,t = N

t = 30 days

Half life of an element =$t_{\frac{1}{2}=10 days$

$\lambda=\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{10 days}=0.0693 days^{-1}$

$\log[N]=\log[N_o]-\frac{\lambda t}{2.303}$

$\log[N]=\log[200 g]-\frac{0.0693 days ^{-1}\times 30 days}{2.303}$

N = 25.01 49 g ≈ 25 g

25 g of an element will remain in  the sample.

Answer 2

N=N₀*2^(-t/T)

N₀=200 g
T=10 d
t=30 d

N=200*2^(-30/10)=25 g

25 g will remain