To find the stable isotope formed when radon-222 undergoes a decay chain of four alpha decays followed by four beta decays, we can follow the decay steps and determine the resulting isotope at each step.
Starting with radon-222 (Radon-222 → Decay 1), it undergoes an alpha decay to produce polonium-218.
Polonium-218 (Decay 2) undergoes another alpha decay to produce lead-214.
Lead-214 (Decay 3) undergoes yet another alpha decay to produce bismuth-210.
Bismuth-210 (Decay 4) goes through alpha decay again to produce thallium-206.
Finally, thallium-206 (Decay 5) undergoes four beta decays to produce lead-206, which is a stable isotope.
Therefore, the stable isotope formed after these decay steps is lead-206.
So, the answer to question 3 is (C) lead-206.
Moving on to question 4, we have the fission of uranium-235. The equation provided is:
235/92 U + 1/0 n -> 90/38 Sr + A/Z X + 2 1/0 n + y
In this equation, 235/92 U represents the uranium-235 nucleus, 1/0 n represents a neutron, 90/38 Sr represents strontium-90, A/Z X represents the unknown product nucleus, 2 1/0 n represents two neutrons, and y represents some form of radiation (such as gamma radiation).
In this fission reaction, the sum of the mass numbers and atomic numbers on both sides of the equation should be equal to each other to maintain a balanced nuclear equation.
The mass number on the left side is 235 (from uranium-235) and the mass number on the right side is 90 (from strontium-90) + A (from the unknown product nucleus) + 2 (from two neutrons). Therefore, the sum of the mass numbers on the right side is 90 + A + 2.
Similarly, the atomic number on the left side is 92 (from uranium-235) and the atomic number on the right side is 38 (from strontium-90) + Z (from the unknown product nucleus). Therefore, the sum of the atomic numbers on the right side is 38 + Z.
Based on the above information, we can conclude that A + 2 = 235 and Z = 92 - 38.
Solving A + 2 = 235 gives A = 233.
Substituting the value of A into Z = 92 - 38 gives Z = 54.
Therefore, the unknown product nucleus represented by A/Z X is 233/54 Xe.
So, the answer to question 4 is (A) 146/54 Xe.
I hope this helps you understand the questions! Let me know if you have any further queries.