You are experimenting with a radioactive sample of polonium. At the end of 14.0 minutes, exactly 1/16 of the polonium remains. The corresponding half-life, T2 , of polonium is: a. 0.875 minutes. b. 1.14 minutes. c. 1.75 minutes. d. 3.50 minutes. e. 4.67 minutes.
Radioactive decay
The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. This periodic table's elements come in a variety of shapes and sizes. Several of these kinds are stable like nitrogen-14, hydrogen-2, and potassium-40, whereas others are not like uranium-238. In nature, one of the most stable phases of an element is usually the most prevalent. Every element, meanwhile, has an unstable state. Unstable variants are radioactive and release ionizing radiation. Certain elements, including uranium, have no stable forms and are constantly radioactive. Radionuclides are elements that release ionizing radiation.
Artificial Radioactivity
The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.
![### Radioactive Decay Question
**Problem Statement:**
You are experimenting with a radioactive sample of polonium. At the end of 14.0 minutes, exactly 1/16 of the polonium remains. The corresponding half-life, \( T_{1/2} \), of polonium is:
**Options:**
a. 0.875 minutes
b. 1.14 minutes
c. 1.75 minutes
d. 3.50 minutes
e. 4.67 minutes
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**Discussion and Analysis:**
To solve this problem, we need to understand the concept of half-life in radioactive decay. The half-life (\( T_{1/2} \)) of a substance is the time required for half of the radioactive atoms in a sample to decay.
Given that exactly 1/16 of the polonium remains after 14.0 minutes, we can use the half-life formula:
\[ \left(\frac{1}{2}\right)^n = \frac{1}{16}, \]
where \( n \) is the number of half-lives that have passed.
Since \( 1/16 = (1/2)^4 \), we can see that:
\[ n = 4 \]
This means that 4 half-lives have passed in 14.0 minutes. Now, we calculate the half-life \( T_{1/2} \):
\[ T_{1/2} = \frac{14.0 \text{ minutes}}{4} = 3.5 \text{ minutes} \]
Thus, the corresponding half-life \( T_{1/2} \) of polonium is:
**Answer:**
d. 3.50 minutes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0959128f-1417-4f4f-bd20-8f81c7fe5d61%2Fce34eb14-63af-451a-931b-0f6759c0a01f%2Fi4hegqq.png&w=3840&q=75)
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