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Math for Test

Math for Test. Chem. New half life equation. Mt=Mo/2(t1/2) Where Mt is final, Mo is initial, and t 1/2 is half-life Half-life is given the symbol t½ Different radioisotopes have different half-lives. The amount of radioactive isotope remaining can be calculated:

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Math for Test

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  1. Math for Test Chem

  2. New half life equation • Mt=Mo/2(t1/2) • Where Mt is final, Mo is initial, and t1/2 is half-life • Half-life is given the symbol t½ • Different radioisotopes have different half-lives. • The amount of radioactive isotope remaining can be calculated: • Nt = No x (0.5)number of half-lives • Where: • Nt = amount of radioisotope remaining • No = original amount of radioisotope • number of half-lives = time ÷ half-life

  3. Half life example (old way) • The isotope Bismuth-212 has a half-life of 8853.66 hours. What mass of a 2.00 mg sample of 212Bi will remain after 3750 hours?  • Now we use the half-life equation: A = Ao x (1/2)^(t/h) Where A is amount remaining at time t, Ao is the original amount, and h is the half-life. A = 2.00 mg x (1/2)^(3750 hrs / 8853.66 hrs) A = 2.00 mg x (1/2)^0.424 A = 2.00 mg x 0.746 A = 1.49 mg  • Or A= 2.00mg x 2 ^ (-t/ half life)

  4. Half life (Different way) • The isotope Bismuth-212 has a half-life of 8853.66 hours. What mass of a 2.00 mg sample of 212Bi will remain after 3750 hours?  • Nt = No x (0.5)number of half-lives • Where: • Nt = amount of radioisotope remaining • No = original amount of radioisotope • number of half-lives = time ÷ half-life • Nt= 2.00mg x (0.5)(.4235) • NNt= 1.49

  5. Alpha Decay • Releases a He atom • 42He • You lose 2 from the atomic number and 4 from the mass number • 24195Am → 23793Np + 42He

  6. Beta Decay • Beta decay occurs when, in a nucleus with too many protons or too many neutrons, one of the protons or neutrons is transformed into the other. • In beta minus decay, a neutron decays into a proton, an electron, and an antineutrino. • The proton stays within the nucleus and gives you the addition to the atomic number, the electron is expelled from the atom.

  7. Beta Decay Math • 146C  147 N + 0-1e • But what you need to know is that a proton adds to the atomic number and jumps up on the periodic table to a new element.

  8. You Try! • If 100.0 g of carbon-14 decays until only 25.0 g of carbon is left after 11 460 y, what is the half-life of carbon-14? • Thallium-208 has a half-life of 3.053 min. How long will it take for 120.0 g to decay to 7.50 g? • Gold-198 has a half-life of 2.7 days. How much of a 96 g sample of gold-198 will be left after 8.1 days? • Potassium-42 has a half-life of 12.4 hours. How much of an 848 g sample of potassium-42 will be left after 62.0 hours?

  9. Average Atomic Mass • If chlorine has two naturally-occurring isotopes where: • Cl-35 mass is 34.96 and is %75 abundantCl-37 mass is 36.96 and is %25 abundant • What is the Average atomic mass?

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