(a) Given that the energy released per fission of 235U nucleus is 200MeV, calculate (i) the number of fissions and (ii) the amount of energy (in joules) available if 50g of 235U is completely fissioned.
(b) A widespread application of nuclear physics is present in many homes in the form of a smoke detector. Discuss the operation of such a smoke detector.
(a) To calculate the number of fissions and the amount of energy released, we need to follow these steps:
(i) Calculate the number of fissions:
- Convert the mass of 235U (50g) to moles using the molar mass of uranium-235. The molar mass of uranium-235 is approximately 235 g/mol.
- Using Avogadro's number (6.022 x 10^23), calculate the number of uranium-235 atoms in moles.
- Each uranium-235 atom undergoes one fission. Therefore, the number of fissions is equal to the number of uranium-235 atoms.
(ii) Calculate the amount of energy:
- Multiply the number of fissions obtained in step (i) by the energy released per fission (200 MeV).
- Convert the energy from MeV to joules using the conversion factor: 1 MeV = 1.6 x 10^-13 joules.
(b) A smoke detector uses a small amount of radioactive material, such as americium-241, which emits alpha particles. The operation of a smoke detector involves the following steps:
1. Ionization: The americium-241 emits alpha particles, which collide with and ionize the surrounding air molecules.
2. Electrical Current: The ionized particles create a small electrical current when they come into contact with a metal plate or wire, creating a continuous flow of electric charge.
3. Smoke Detection: When smoke particles enter the smoke detector, they disrupt the flow of ions and electric current. This change in current is detected by a sensor.
4. Alarm Trigger: The disrupted current triggers the smoke detector's alarm, alerting occupants to the presence of smoke.
Smoke detectors are an effective means of fire detection as they can detect the early stages of a fire and provide early warning to occupants, enabling them to evacuate and seek safety.