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A radioactive isotope has a half life of 1.2 billion years. As measguard by the presence of the isotope and its stable decay product, a rock originally contained 10g of the radioactive isotope and now contains 1.25 g.How many years old is the rock?
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A radioactive isotope has a half life of 1.2 billion years. As measgua...
Calculating the Age of the Rock with Radioactive Isotope

To calculate the age of the rock containing a radioactive isotope, we need to use the concept of half-life and radioactive decay.

Half-Life and Radioactive Decay

The half-life of a radioactive isotope is the time it takes for half of the initial amount of the isotope to decay. The rate of decay of a radioactive isotope is constant and is measured by its half-life.

Calculating the Age of the Rock

We know from the problem statement that the original amount of the radioactive isotope in the rock was 10g and the current amount is 1.25g. We can use the formula for decay of a radioactive substance to calculate the age of the rock.

The formula for decay of a radioactive substance is:

N = N0 * (1/2)^(t/T)

where N is the current amount of the isotope, N0 is the initial amount of the isotope, t is the time that has passed, and T is the half-life of the isotope.

Substituting the given values in the formula, we get:

1.25 = 10 * (1/2)^(t/1.2 billion)

Taking natural logarithm on both sides of the equation, we get:

ln(1.25/10) = (t/1.2 billion) * ln(1/2)

Solving for t, we get:

t = (ln(1.25/10) / ln(1/2)) * 1.2 billion

t ≈ 3.6 billion years

Therefore, the rock is approximately 3.6 billion years old.

Conclusion

To calculate the age of a rock containing a radioactive isotope, we need to use the concept of half-life and radioactive decay. By using the decay formula and given values, we can calculate the age of the rock. In this case, the rock is approximately 3.6 billion years old.
Community Answer
A radioactive isotope has a half life of 1.2 billion years. As measgua...
3.6 billion years
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Read the following text and answer the following questions on the basis of the same:Microwave oven:The spectrum of electromagnetic radiation contains a part known as microwaves. These waves have frequency and energy smaller than visible light and wavelength larger than it. What is the principle of a microwave oven and how does it work ? Our objective is to cook food or warm it up. All food items such as fruit, vegetables, meat, cereals, etc., contain water as a constituent. Now, what does it mean when we say that a certain object has become warmer? When the temperature of a body rises, the energy of the random motion of atoms and molecules increases and the molecules travel or vibrate or rotate with higher energies. The frequency of rotation of water molecules is about 2.45 gigahertz (GHz). If water receives microwaves of this frequency, its molecules absorb this radiation, which is equivalent to heating up water. These molecules share this energy with neighbouring food molecules, heating up the food. One should use porcelain vessels and non metal containers in a microwave oven because of the danger of getting a shock from accumulated electric charges. Metals may also melt from heating. The porcelain container remains unaffected and cool, because its large molecules vibrate and rotate with much smaller frequencies, and thus cannot absorb microwaves. Hence, they do not get eaten up. Thus, the basic principle of a microwave oven is to generate microwave radiation of appropriate frequency in the working space of the oven where we keep food. This way energy is not wasted in heating up the vessel. In the conventional heating method, the vessel on the burner gets heated first and then the food inside gets heated because of transfer of energy from the vessel. In the microwave oven, on the other hand, energy is directly delivered to water molecules which are shared by the entire food.Q. Why should one use porcelain vessels and non- metal containers in a microwave oven ?

Read the following text and answer the following questions on the basis of the same:Microwave oven:The spectrum of electromagnetic radiation contains a part known as microwaves. These waves have frequency and energy smaller than visible light and wavelength larger than it. What is the principle of a microwave oven and how does it work ? Our objective is to cook food or warm it up. All food items such as fruit, vegetables, meat, cereals, etc., contain water as a constituent. Now, what does it mean when we say that a certain object has become warmer? When the temperature of a body rises, the energy of the random motion of atoms and molecules increases and the molecules travel or vibrate or rotate with higher energies. The frequency of rotation of water molecules is about 2.45 gigahertz (GHz). If water receives microwaves of this frequency, its molecules absorb this radiation, which is equivalent to heating up water. These molecules share this energy with neighbouring food molecules, heating up the food. One should use porcelain vessels and non metal containers in a microwave oven because of the danger of getting a shock from accumulated electric charges. Metals may also melt from heating. The porcelain container remains unaffected and cool, because its large molecules vibrate and rotate with much smaller frequencies, and thus cannot absorb microwaves. Hence, they do not get eaten up. Thus, the basic principle of a microwave oven is to generate microwave radiation of appropriate frequency in the working space of the oven where we keep food. This way energy is not wasted in heating up the vessel. In the conventional heating method, the vessel on the burner gets heated first and then the food inside gets heated because of transfer of energy from the vessel. In the microwave oven, on the other hand, energy is directly delivered to water molecules which are shared by the entire food.Q. As compared to visible light microwave has frequency and energy

A radioactive isotope has a half life of 1.2 billion years. As measguard by the presence of the isotope and its stable decay product, a rock originally contained 10g of the radioactive isotope and now contains 1.25 g.How many years old is the rock?
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A radioactive isotope has a half life of 1.2 billion years. As measguard by the presence of the isotope and its stable decay product, a rock originally contained 10g of the radioactive isotope and now contains 1.25 g.How many years old is the rock? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A radioactive isotope has a half life of 1.2 billion years. As measguard by the presence of the isotope and its stable decay product, a rock originally contained 10g of the radioactive isotope and now contains 1.25 g.How many years old is the rock? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radioactive isotope has a half life of 1.2 billion years. As measguard by the presence of the isotope and its stable decay product, a rock originally contained 10g of the radioactive isotope and now contains 1.25 g.How many years old is the rock?.
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