Answers:
1)The correct answer is 3g.
2)The correct answer is approximately 1.3.
3)The correct answer is 10.
1)
Step-by-step explanation:
Manganese-56 has a half-life of 2.6 hours, which means that after 2.6 hours, half of the original amount of manganese-56 will have decayed. We can use this information to determine how much manganese will remain after 7.8 hours, starting with 20g of manganese.
Number of half-lives that have passed:
7.8 hours ÷ 2.6 hours/half-life = 3 half-lives
Amount of manganese remaining:
After 1 half-life: 20g / 2 = 10g
After 2 half-lives: 10g / 2 = 5g
After 3 half-lives: 5g / 2 = 2.5g
Therefore, 20g - 2.5g = 17.5g of manganese will have disappeared after 7.8 hours.
2)
Step-by-step explanation:
The neutron to proton ratio for a stable nucleus is not constant, but there is a general trend known as the band of stability. According to the band of stability, stable nuclei have a neutron to proton ratio that increases with increasing atomic mass number.
Vanadium has an atomic number of 23, which means it has 23 protons in its nucleus. To determine the approximate neutron to proton ratio for vanadium, we can look at the neighboring stable nuclei on the band of stability. The stable isotopes closest to vanadium are chromium-50 and manganese-55, which have neutron to proton ratios of approximately 1.4 and 1.3, respectively.
Since vanadium is closer in atomic mass to manganese-55, we can approximate its neutron to proton ratio to be similar to that of manganese-55, which is approximately 1.3.
3)
Step-by-step explanation:
Radon-222 has a half-life of 3.8 days, which means that after 3.8 days, half of the original amount of radon-222 will have decayed. We can use this information to determine how many half-lives will pass after 38 days.
Number of half-lives that have passed:
38 days ÷ 3.8 days/half-life = 10 half-lives
After 10 half-lives, the amount of radon-222 remaining will be:
(1/2)^10 = 1/1024 of the original amount.
This means that 1023/1024 of the original amount of radon-222 will have decayed after 38 days, which is approximately 99.9023%.