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Vinil7 [7]
3 years ago
10

How are half life and radioactive decay related

Chemistry
1 answer:
hoa [83]3 years ago
3 0

Answer : Half life and radioactive decay are inversely proportional to each other.

Explanation :

The mathematic relationship between the half-life and radioactive decay :

N=N_oe^{-\lambda t}              ................(1)

where,

N = number of radioactive atoms at time, t

N_o = number of radioactive atoms at the beginning when time is zero

e = Euler's constant = 2.17828

t = time

\lambda = decay rate

when t=t_{1/2} then the number of radioactive decay become half of the initial decay atom i.e N=\frac{N_o}{2}.

Now substituting these conditions in above equation (1), we get

\frac{N_o}{2}=N_oe^{-\lambda t_{1/2}}

By rearranging the terms, we get

\frac{1}{2}=e^{-\lambda t_{1/2}}

Now taking natural log on both side,

ln(\frac{1}{2})=-\lambda \times t_{1/2}

By rearranging the terms, we get

t_{1/2}=\frac{0.693}{\lambda}

This is the relationship between the half-life and radioactive decay.

Hence, from this we conclude that the Half life and radioactive decay are inversely proportional to each other. That means faster the decay, shorter the half-life.

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<h3>General Formulas and Concepts:</h3>

<u>Math</u>

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Chemistry</u>

<u>Atomic Structure</u>

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<u>Stoichiometry</u>

  • Using Dimensional Analysis
<h3>Explanation:</h3>

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[Solve] grams (mass) SO₂

<u>Step 2: Identify Conversions</u>

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[PT] Molar Mass of O - 16.00 g/mol

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<u>Step 3: Convert</u>

  1. [DA] Set up:                                                                                                     \displaystyle 2.16 \ mol \ SO_2(\frac{64.07 \ g \ SO_2}{1 \ mol \ SO_2})
  2. [DA] Multiply/Divide [Cancel out units]:                                                         \displaystyle 138.391 \ g \ SO_2

<u>Step 4: Check</u>

<em>Follow sig fig rules and round. We are given 3 sig figs.</em>

138.391 g SO₂ ≈ 138 g SO₂

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