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

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

Answer 2

25 g of an element will remain in the sample.

Step-by-step 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_{(1)/(2)=10 days`

`\lambda=\frac{0.693}{t_{(1)/(2)}}=(0.693)/(10 days)=0.0693 days^(-1)`

`\log[N]=\log[N_o]-(\lambda t)/(2.303)`

`\log[N]=\log[200 g]-(0.0693 days ^(-1)* 30 days)/(2.303)`

N = 25.01 49 g ≈ 25 g

25 g of an element will remain in the sample.