NCERT

Photons do not have enough energy ( )to overcome the work function (? ) of the material below the threshold frequency.The energy per photon remains too low to liberate electrons even if the light intensity is increased, so photoelectric emission cannot occur.

According to de Broglie's hypothesis, all matter exhibits wave-like behavior. It laid the foundation for quantum mechanics by introducing the concept of matter waves. The dual nature of particles (both wave and particle) is essential in designing technologies like electron microscopes and helps explain phenomena like electron diffraction.

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According to Bohr's postulates, in specific stable orbits, electrons revolve without emitting energy. Energy is only absorbed or emitted when electrons jump between these orbits, preventing them from spiraling into the nucleus.

The concept of quantized energy levels for electrons in atoms is introduced by Bohr's model. Although, Bohr's model could not explain the spectra of multi-electron atoms. It helped lay the foundation for quantum mechanics and successfully explained the spectral lines of hydrogen.

These are the difference between the alpha, beta and gamma decay:

• Alpha decay: It reduces mass number by 4 and atomic number by 2. It is the emission of a helium nucleus (2 protons, 2 neutrons).
• Beta decay: It changes atomic number by ±1 but there is no change in the mass number. It involves a neutron converting into a proton (or vice versa).
• Gamma decay: Here, there is no change in the atomic or mass number, just the emission of high-energy photons.

Within a nucleus, how tightly nucleons are bound is the binding energy per nucleon. If the binding energy per nucleon is higher then it means more stable nuclei. Iron-56 is the most stable as it has one of the highest values. Both the fusion of light nuclei and the fission of heavy nuclei release energy by moving toward higher binding energy per nucleon.

The difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons is known as the mass defect. Mass defect is the key concept in understanding the nuclear stability and energy release in nuclear reactions. The binding energy is converted from the "missing" mass. The binding energy holds the nucleus together. 

A single slit diffraction pattern produces a central maximum and diminishing side bands as it interacts with itself and results from the wavefront bending around the edges of the slit. However, the double slit interference pattern forms equally spaced bright and dark fringes, and it is due to the light superposition from two different coherent sources.

The following conditions are needed to observe sustained (stable) interference:

• The two sources should have a constant phase difference, i.e; they should be coherent.
• The light waves need to have almost the same frequencies.
• The sources must emit waves with comparable amplitudes.
• The path difference should be within the coherence length.