Modern Physics

The energy of a photon is related to its momentum and frequency by the equation: Thus, the frequency associated with the photon is given by .

Let the initial amount of the substance be .
The percentage decayed after 5 years is 10%, so the remaining percentage after 5 years is 90%.
This is the same as saying: After another 5 years (i.e., 10 years in total), the remaining amount is 90% of , so: After 15 years, the remaining amount is: After 20 years, the remaining amount is: Now, we calculate the percentage decayed after 20 years:
Thus, the correct answer is (d).

The number of undecayed nuclei after a time mean lives is given by the decay law: where is the decay constant and is the time, with being the mean life. In terms of the fraction of undecayed nuclei, we can express the number of remaining nuclei after mean lives as:
Thus, the correct answer is (a).

The de-Broglie wavelength of a particle is given by the equation: where is Planck’s constant, is the mass of the particle, is the charge of the particle, and is the potential difference.
For electrons and protons, their respective wavelengths are: Since the potential difference is the same (4 V), the ratio is:
Thus, the correct answer is (d).

The number of neutrons released during the fission reaction of uranium-235 is typically 4. This is a known value for the fission of uranium isotopes, where a single fission event of uranium-235 generally produces 2 to 3 neutrons, but on average, it is 4 neutrons that are released. These neutrons can go on to initiate further fission reactions, leading to a chain reaction. This process is a fundamental aspect of nuclear reactors and nuclear weapons.

Hence, the correct answer is (c).