The radon-222 sample has a half-life of 3.8 days, and we are asked how many times would the mass divide in half after 23 days. First we calculate the amount of times division occurs by taking the number of days and dividing that by the number of days for one half-life to occur: 23/3.8 = 6.05.
We have 198.6 grams of sample, and we are going to divide it in half 6 times to determine how much of it remains after 23 days:
198.6/2 = 99.3 grams
99.3/2 = 49.65 grams
49.65/2 = 24.83 grams
24.83/2 = 12.41 grams
12.41/2 = 6.21 grams
6.21/2 = 3.1 grams
Therefore, we are left with 3.1 grams of radon-222 after 23 days if one half-life equals to 3.8 days.
The amount of energy released when 0.06 kg of mercury condenses at the same temperature can be calculated using its latent heat of fusion which is the opposite of melting. Latent heat of fusion and melting can be used because they have the same magnitude, but opposite signs. Latent heat is the amount of energy required to change the state or phase of a substance. For latent heat, there is no temperature change. The equation is:
E = m(ΔH)
where:
m = mass of substance
ΔH = latent heat of fusion or melting
According to data, the ΔH of mercury is approximately 11.6 kJ/kg.
E = 0.06kg (11.6 kJ/kg) = 0.696 kJ or 696 J
The answer is D. 697.08 J. Note that small differences could be due to rounding off or different data sources.
214.0560
+ 9.3456
=223.4016
