Radioactivity and radioactive decay

In summary, the problem involves thorium undergoing alpha decay to produce radium. To find the percent of thorium left after 266 days, we can use the equation N=No*(1/2)^n, where n is the number of half-lives. Since 266 days is less than the half-life of thorium, more than 50% should be left. Therefore, the answer is 36%.
  • #1
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[SOLVED] Radioactivity and radioactive decay

Homework Statement


Thorium (with half-life T1/2 = 1.913 yr. and atomic mass 228.028715 u) undergoes alpha decay and produces radium (atomic mass 224.020186 u) as a daughter nucleus. (Assume the alpha particle has atomic mass 4.002603 u.)

What percent of thorium is left after 266 days?



Homework Equations



X --> Y + He
N=No*(1/2)^n
n= t/T(half)
T(half)= .693/[tex]\lambda[/tex]


The Attempt at a Solution



I found that lambda=4.14x10^-5 hrs^-1 (the problem asks for it in hours, dumb, I know.)

I then found the number of half-lives to be 266 days, or 6384 hours divided by 16757.88 hours, to be .381 half-lives. I multiplied this by Thorium's atomic mass to get 36% but this keeps turning up incorrect for my online homework.
 
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  • #2
Why don't you just apply N=No*(1/2)^n ?

since 266 days is shorter than the half life, more than 50% should be left.
 
  • #3
Ahhhhh for some reason I thought I needed to now the number of nuclei, did NOT know I could just use the atomic mass. I got it, thank you!
 

1. What is radioactivity?

Radioactivity is the process by which an unstable atomic nucleus emits energy and particles in order to become more stable. This process is also known as radioactive decay or nuclear decay.

2. How is radioactivity measured?

Radioactivity is measured using a unit called the becquerel (Bq), which represents the number of radioactive decays per second. Another commonly used unit is the curie (Ci), which represents the number of decays per second in a specific amount of a radioactive material.

3. What are the different types of radioactive decay?

The three most common types of radioactive decay are alpha decay, beta decay, and gamma decay. In alpha decay, an alpha particle (consisting of two protons and two neutrons) is emitted from the nucleus. In beta decay, a beta particle (either an electron or a positron) is emitted from the nucleus. In gamma decay, a high-energy photon is emitted from the nucleus.

4. What are the dangers of exposure to radioactivity?

Exposure to high levels of radioactivity can be harmful to living organisms, as it can damage cells and DNA. This can lead to health problems such as cancer and radiation sickness. However, low levels of exposure are typically not harmful and are even used in medical procedures such as X-rays.

5. How is radioactivity used in everyday life?

Radioactivity has many practical applications in everyday life. It is used in smoke detectors, medical imaging, and cancer treatment. It is also used in nuclear power plants to generate electricity. Additionally, radioactive materials are used in scientific research and to date archaeological artifacts.

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