Answer :
Answer:
15.63 grams
Step-by-step explanation:
To find the amount of Astatine-218 left after 10 seconds, we'll use the formula for exponential decay:
[tex]\Large\boxed{\boxed{\sf N = N_0 \times \left( \dfrac{1}{2} \right)^{\frac{t}{T}}}} [/tex]
Where:
- [tex]\sf N [/tex] is the final amount of Astatine-218.
- [tex]\sf N_0 [/tex] is the initial amount of Astatine-218 (500 grams in this case).
- [tex]\sf t [/tex] is the elapsed time (10 seconds in this case).
- [tex]\sf T [/tex] is the half-life of Astatine-218 (2 seconds in this case).
Substituting the given values:
[tex]\sf N = 500 \times \left( \dfrac{1}{2} \right)^{\frac{10}{2}} [/tex]
[tex]\sf N = 500 \times \left( \dfrac{1}{2} \right)^5 [/tex]
[tex]\sf N = 500 \times \left( \dfrac{1}{32} \right) [/tex]
[tex]\sf N = \dfrac{500}{32} [/tex]
[tex]\sf N \approx 15.625 [/tex]
[tex]\sf N \approx 15.63 \textsf{ grams (in nearest hundredth)} [/tex]
So, the amount of Astatine-218 left from a 500-gram sample after 10 seconds is approximately 15.63 grams.
