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A radioactive element has a half-life of 10 days. If you start with a 100 gram sample, approximately how much of the element will remain after 30 days, considering the principles of radioactive decay?
A radioactive element has a half-life of 10 days. If you start with a 100 gram sample, approximately how much of the element will remain after 30 days, considering the principles of radioactive decay?
- 25 grams
- 12.5 grams (correct)
- 33.3 grams
- 50 grams
Consider two radioactive isotopes, Isotope A with a decay constant $\lambda_A$ and Isotope B with a decay constant $\lambda_B$, where $\lambda_A > \lambda_B$. What can be inferred about their half-lives and decay rates?
Consider two radioactive isotopes, Isotope A with a decay constant $\lambda_A$ and Isotope B with a decay constant $\lambda_B$, where $\lambda_A > \lambda_B$. What can be inferred about their half-lives and decay rates?
- Isotope A has a shorter half-life but decays more slowly than Isotope B.
- Isotope A has a shorter half-life and decays more rapidly than Isotope B. (correct)
- Isotope A has a longer half-life but decays more rapidly than Isotope B.
- Isotope A has a longer half-life and decays more slowly than Isotope B.
A sample of a radioactive isotope initially contains $N_0$ atoms. After a time period equal to two half-lives, which of the following expressions correctly represents the number of radioactive atoms remaining in the sample?
A sample of a radioactive isotope initially contains $N_0$ atoms. After a time period equal to two half-lives, which of the following expressions correctly represents the number of radioactive atoms remaining in the sample?
- $N_0/\lambda$
- $N_0/2$
- $N_0/e^2$
- $N_0/4$ (correct)
If the number of radioactive atoms decaying in a time interval $\Delta t$ is given by $\Delta N = -\lambda N \Delta t$, what does the negative sign signify in this equation?
If the number of radioactive atoms decaying in a time interval $\Delta t$ is given by $\Delta N = -\lambda N \Delta t$, what does the negative sign signify in this equation?
Consider a scenario where a radioactive substance initially has $10^{6}$ atoms and a decay constant of $0.01 s^{-1}$. Determine the approximate number of atoms that will decay in the first second.
Consider a scenario where a radioactive substance initially has $10^{6}$ atoms and a decay constant of $0.01 s^{-1}$. Determine the approximate number of atoms that will decay in the first second.
Consider two radioactive isotopes, X and Y. Isotope X has a decay constant $\lambda_X$ and isotope Y has a decay constant $\lambda_Y = 2\lambda_X$. After a certain time period, what is the ratio of the number of half-lives of isotope X to the number of half-lives of isotope Y?
Consider two radioactive isotopes, X and Y. Isotope X has a decay constant $\lambda_X$ and isotope Y has a decay constant $\lambda_Y = 2\lambda_X$. After a certain time period, what is the ratio of the number of half-lives of isotope X to the number of half-lives of isotope Y?
A sample of a radioactive element initially contains $N_0$ atoms. After a certain period, it's found that the number of atoms has reduced to $\frac{N_0}{8}$. How many half-lives have passed during this period?
A sample of a radioactive element initially contains $N_0$ atoms. After a certain period, it's found that the number of atoms has reduced to $\frac{N_0}{8}$. How many half-lives have passed during this period?
A radioactive sample has a half-life of $T$. If you start with a sample of $N_0$ atoms, how many atoms will have decayed after a time period of $2T$?
A radioactive sample has a half-life of $T$. If you start with a sample of $N_0$ atoms, how many atoms will have decayed after a time period of $2T$?
Consider two radioactive isotopes, A and B, with half-lives of 5 years and 10 years, respectively. If you start with the same number of atoms of each isotope, after how many years will the activity of A be approximately four times greater than that of B?
Consider two radioactive isotopes, A and B, with half-lives of 5 years and 10 years, respectively. If you start with the same number of atoms of each isotope, after how many years will the activity of A be approximately four times greater than that of B?
Which of the following statements is NOT correct regarding artificial radioactivity?
Which of the following statements is NOT correct regarding artificial radioactivity?
Flashcards
Half-life
Half-life
The time it takes for half of the radioactive atoms in a sample to decay.
Radioactive Decay
Radioactive Decay
Radioactive decay where an element transforms into another element by emitting alpha or beta particles.
Complete Decay
Complete Decay
No radioactive element ever fully decays; there will always be a remaining amount.
Decay Constant
Decay Constant
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Decay Constant Definition
Decay Constant Definition
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Decay Curve
Decay Curve
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Atoms after n half-lives
Atoms after n half-lives
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Half-life Variation
Half-life Variation
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λ and T1/2 Relation
λ and T1/2 Relation
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Study Notes
- The half-life of a radioactive element refers to the period in which half of its atoms decay.
- When alpha or beta particles are emitted, a radioactive element transforms into another element.
- Radioactive decay is a random process.
Radioactive Decay
- It's impossible for a radioactive element to completely decay as only half of the nuclei decay in each half-period, requiring infinite time for all atoms to decay.
- The number of atoms decaying in a specific period is proportional to the number of atoms at the start; more atoms at the beginning mean more decay during that period.
- Equations can represent these results, where ΔN is proportional to the time interval Δt and the number of atoms N at a particular time.
- ΔN ∝ -N
- ΔN ∝ Δt
- ΔN ∝ -NΔt
- ΔN = -Constant N Δt
- ΔN = -λNΔt
- λ, the decay constant, is the proportionality constant, and the negative sign indicates the decrease in the number of atoms N.
Decay Constant
- If the decay constant λ is large, more atoms will decay in a particular interval.
- If the decay constant λ is small, fewer atoms will decay.
- λ = - (ΔN/N) / Δt
- The ratio of the fraction of decaying atoms per unit time is called the decay constant.
- The SI unit of decay constant is s⁻¹.
Decay Curve
- Graphing the number of radioactive elements decaying at a particular rate over time yields a decay curve.
Determination of Half-Life
- In the beginning the number of atoms present in the sample = N₀
- After one half-life, the remaining number of atoms = (1/2)N₀
- After two half-lives, the remaining number of atoms = (1/4)N₀ = (1/2)² N₀
- After three half-lives, the remaining number of atoms = (1/8)N₀ = (1/2)³ N₀
Estimation of Half-Life
- Different elements have different half-life values.
- The half-life of uranium-238 is 4.5 × 10⁹ years.
- The half-life of radium-226 is 1620 years.
- The half-life of radon is 3.8 days.
- The half-life of uranium-239 is 23.5 minutes.
Relationship between λ and T₁/₂
- The decay constant λ and half-life T₁/₂ have the following relationship: λ × T₁/₂ = 0.693
- T₁/₂ = 0.693 / λ
- Knowing the decay constant λ of a radioactive element allows determination of its half-life.
Artificial Radioactivity
- Any stable element can be made radioactive by bombarding it with a high-energy particle; this excites the nucleus, turning the element radioactive.
- These artificially created radioactive elements are called artificial radioactive elements.
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Description
Explanation of radioactive decay, the concept of half-life, and the decay constant. Radioactive elements transform when emitting alpha or beta particles. Radioactive decay is a random process where the number of decaying atoms is proportional to the initial number of atoms.
