NCERT

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.

Young's Double-Slit Experiment demonstrates the interference phenomenon. It provides strong proof for the wave nature of light. This experiment shows how due to constructive and destructive interference, two coherent light sources create a pattern of bright and dark fringes.

The image is real when it is formed by the actual convergence of rays and it can be projected on a screen. For example, when the object is placed beyond focus, and the image is formed either by the convex lens or concave mirror.
The image is virtual, if it is formed by the apparent divergence of rays and it cannot be captured on a screen. For example, when the image is formed by the convex mirror or plane mirror.

Simple microscope: When the object is placed within the focal length, the simple microscope works on the principle of producing an erect, virtual and magnified image. To magnify small objects, the simple microscope uses a single convex lens.
Compound microscope: It uses two lenses including an eyepiece and objective. The objective lens creates a real, magnified, and inverted image which acts as the object for the eyepiece, which in turn magnifies it further.

In Ray Optics And Optical Instruments questions, when using lens and mirror formulas, sign convention helps in maintaining consistency. The sign convention determines whether quantities like image distance, object distance, and focal length are taken as positive or negative. The incorrect usage of these sign conventions mostly leads to wrong magnifications and image positions. For accurate results, it is essential to follow the Cartesian sign.