Answer:
The half life of element XY is 12 days
Explanation:
Given:
Time taken for 1024 grams to decay into 32 grams = 60 days
To Find:
The half life of element XY = ?
Solution:
The Half life is calculated by
[tex]N = N_0 (\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}[/tex]
[tex]t_{\frac{1}{2}}[/tex] =[tex]\frac{t}{log_{\frac{1}{2}}( \frac{N(t)}{N_0})}}[/tex]
Substituting the values,
[tex]t_{\frac{1}{2}}[/tex] =[tex]\frac{60}{log_{\frac{1}{2}}( \frac{32}{1024})}}[/tex]
[tex]t_{\frac{1}{2}}[/tex] =[tex]\frac{60}{log_{\frac{1}{2}}(0.03125)}}[/tex]
[tex]t_{\frac{1}{2}}[/tex] =[tex]\frac{60}{5}[/tex]
[tex]t_{\frac{1}{2}}[/tex] = 12
