Law of Radioactive Decay – Class 12 | Chapter – 13 | Physics Short Notes Series PDF for NEET & JEE

Law of Radioactive Decay: The Law of Radioactive Decay states that the rate at which a radioactive substance decays is proportional to the number of atoms present. This means that the more atoms of a radioactive substance there are, the faster the rate of decay. The law can be expressed mathematically as:

N(t) = N0 * e-λt

where N(t) is the number of radioactive atoms remaining at time t, N0 is the initial number of radioactive atoms, e is the mathematical constant 2.71828…, λ is the decay constant (a characteristic of the particular radioactive substance), and t is the elapsed time.

The law of radioactive decay is important because it allows scientists to predict the rate at which a radioactive substance will decay over time. This information is useful in many fields, including nuclear power generation, medical imaging, and radiocarbon dating. By knowing the rate of radioactive decay, scientists can determine how long a radioactive substance will remain active and how much radiation it will emit during that time. This information can help to ensure the safe handling and disposal of radioactive materials.

Types of Radioactive Decay

There are three main types of radioactive decay: alpha decay, beta decay, and gamma decay.

• Alpha decay: In alpha decay, a heavy nucleus emits an alpha particle, which consists of two protons and two neutrons. This reduces the mass number of the nucleus by four and the atomic number by two. Alpha decay is common in very heavy elements, such as uranium and radium.
• Beta decay: In beta decay, a nucleus emits a beta particle, which can be either an electron or a positron. This changes the atomic number of the nucleus, but not the mass number. Beta decay is common in elements with too many or too few neutrons, which can be corrected by converting a neutron into a proton (beta minus decay) or a proton into a neutron (beta plus decay).
• Gamma decay: In gamma decay, a nucleus emits a gamma ray, which is a high-energy photon. Gamma decay does not change the atomic number or mass number of the nucleus, but it reduces its energy level. Gamma decay often follows alpha or beta decay, as the resulting nucleus may be in an excited state.

Applications of Law of Radioactive Decay

The Law of Radioactive Decay has many practical applications in a variety of fields, including:

• Nuclear Power Generation: The Law of Radioactive Decay is used to predict the rate of decay of nuclear fuel in a nuclear reactor. This information is used to control the rate of the nuclear reaction and ensure safe and efficient power generation.
• Medical Imaging: The Law of Radioactive Decay is used to predict the rate of decay of radioactive isotopes used in medical imaging techniques such as PET (positron emission tomography) and SPECT (single photon emission computed tomography) scans. This information is used to determine the appropriate timing of the scan and ensure accurate results.
• Radiocarbon Dating: The Law of Radioactive Decay is used to determine the age of organic materials, such as fossils or archaeological artifacts. This is done by measuring the rate of decay of radioactive carbon-14 in the sample.
• Radiation Therapy: The Law of Radioactive Decay is used to predict the rate of decay of radioactive isotopes used in radiation therapy for cancer treatment. This information is used to determine the appropriate dosage and timing of the therapy.
• Environmental Monitoring: The Law of Radioactive Decay is used to predict the rate of decay of radioactive isotopes in the environment, such as fallout from nuclear weapons testing or nuclear accidents. This information is used to monitor the level of radiation exposure and ensure public safety.

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