Answer : The fraction represents the amount of an original sample of this element remaining after 6 days is [tex]\frac{1}{8}[/tex] .
Explanation :
Half-life = 2 days
Time = 6 days
Formula used:
[tex]N=N_o\times (\frac{1}{2})^{(\frac{t}{t_{1/2}})}[/tex]
where,
N = final amount
[tex]N_o[/tex] = initial amount
t = time
[tex]t_{1/2}[/tex] = half-life
Now putting all the given values in the above formula, we get:
[tex]N=N_o\times (\frac{1}{2})^{(\frac{6}{2})}[/tex]
[tex]\frac{N}{N_o}=(\frac{1}{2})^{(\frac{6}{2})}[/tex]
[tex]\frac{N}{N_o}=(\frac{1}{2})^3[/tex]
[tex]\frac{N}{N_o}=\frac{1}{8}[/tex]
Therefore, the fraction represents the amount of an original sample of this element remaining after 6 days is [tex]\frac{1}{8}[/tex] .