1. if you have 4.0 g of a radioactive substance left after 4 half-lives have passed, then how much did you have originally? a. 50 g b. 64 g c. 25 g d. 10 g 2. if a fusion reaction yields 4.50 x 10^9 kj of energy, then how much mass was lost? a. 5.00 x 10^-5 kg b. 1.50 x 10^-6 kg c. 1.50 x 10^-3 kg d. 5.00 x 10^-2 kg 3. for the transmutation shown, which of the following is x? (the first number is on top on the actual answer.) a. 3 1 h b. 6 3 li c. 1 1 h d. 4 2 he 5. which of the following energy yields is most likely to have come from a fission or fusion reaction? a. 1.0 x 10^2 kj/mol b. 2.5 x 10^2 kj/mol c. 1.5 x 10^3 kj/mol d. 2.0 x 10^11 kj/mol

Answer 1: 
During the radio-active disintegration, when initial concentration of radioactive nuclei is reduced to half, it is referred as half life.
Now, if initial concentration  of radio-active element is 64 g. After it crosses 1st half life, it concentration will decrease to 32g. At 2nd half life, concentration will further reduce to 16 g. This concentration will reduce to 8 g, at 3 half life. And, finally at 4th half life, concentration of radioactive element will reduce to 4 g. 
Thus ,in present case, correct answer is B 64 g.

Answer 2:
Given that energy produced during nuclear fusion reaction = 4.50 x 10^9 kJ
Now, based on Einstein's Equation, we know that E = mc2
where, E = energy produced
m = mass o f compound
c = speed of light = 3 X 10^8 m/s
Thus, 4.50 x 10^9 x 10^3J = m (3 X 10^8)^2
∴ m = 5 X 10^-5 Kg 

Thus, mass lost in the reaction = 5 X 10^-5 Kg 

Answer 3: 
In nuclear transmutation reaction, a non-radioactive nuclei is collided with a fast moving projectile to convert into radio-active nuclei. Following is the examples of nuclear transmutation reaction
 1 1H + 1 0n   →      2 1 H + gamma rays
 
In the above reaction hydrogen, on collision with neutron generates deuterium.
However, other elements listed above will not undergo nuclear transmutation reaction. 

Answer 4: 
In a nuclear reaction, one nuclei get converted into another nuclei. Nuclear reactions are broadly classified into two types. 
a) Nuclear fusion
b) Nuclear fission
In nuclear fusion reaction, two light nuclei under extreme conditions fuse together, while in nuclear fission reaction, a heavy nuclei is bombarded with projectile which breaks the nuclei in smaller nuclei. In either case, mass of product is less than mass of reactant. Thus there is a mass defect. Due to mass defect, tremendous amount of energy is released from the system which is of order of 10^11 Kj/mol. Thus, correct answer is option D.