State Bohr’s postulate to define stable orbits in hydrogen atom. How does de Broglie’s hypothesis explain the stability of these orbits ?

Bohr's postulate to define stable orbits in hydrogen atoms states that an electron can revolve only in those circular orbits in which its angular momentum is an integral multiple of n h / 2 π , where h is Planck’s constant and n is the principal quantum number of orbit. Thus, an electron can revolve only in certain orbits of definite radii. These are called stable orbits. An atom has a number of stable orbits in which an electron can reside without the emission of radiant energy. Each orbit corresponds, to a certain energy level. De Broglie hypothesis explanation of the stability of orbits: According to de Broglie, an electron orbiting around the nucleus is associated with a stationary wave. Electron wave is a circular standing wave. Since destructive interference will occur if a standing wave does not close upon itself, only those de Broglie waves exist for which the circumference of the circular orbit contains a whole number of wavelengths i.e., the circumference of n t h stable orbit for an electron can contain exactly n wavelength of de-Broglie. ⇒ n λ = 2 πr n n h p = 2 πr n n h m v = 2 πr n m v r n = n h 2 π ⇒ L = n h 2 π This was the quantum condition proposed by Bohr.

A symmetric biconvex lens of the radius of curvature R and made of glass of refractive index 1 . 5 , is placed on a layer of liquid placed on top of a plane mirror as shown in the figure. An optical needle with its tip on the principal axis of the lens is moved along the axis until its real, inverted image coincides with the needle itself. The distance of the needle from the lens is measured to be x . On removing the liquid layer and repeating the experiment, the distance is found to be y . Obtain the expression for the refractive index of the liquid in terms of x and y .

We are given, the refractive index of the lens, μ g = 1 . 5 . The distance of the needle from the lens in the first case is equal to the focal length of the combination of a convex lens and a planoconcave lens formed by the liquid. Thus, f = x The distance measured in the second case is equal to the focal length of the convex lens. Thus, f 1 = y Let f 2 be the focal length of the planoconcave lens formed by the liquid. Then, 1 f = 1 f 1 + 1 f 2 1 f 2 = 1 x - 1 y = y - x x y f 2 = x y y - x Let the radius of curvature of the first surface be R The radius of curvature of the second surface will be - R Thus, for the biconvex lens, 1 f 1 = μ g - 1 1 R - 1 - R 1 y = 1 . 5 - 1 2 R ⇒ y = R Let the refractive index of liquid be μ . For plano-convex lens, R 2 = ∞ R 1 = - R Thus, 1 f 2 = μ - 1 1 - R - 1 ∞ Substituting values from above, y - x x y = μ - 1 1 - y μ - 1 = - ( y - x ) x μ = x - y x + 1 μ = 2 x - y x

State Gauss’ law for magnetism. Explain its significance.

Gauss law for magnetism says that if a closed surface is imagined in a magnetic field, the number of lines of force emerging from the surface must be equal to the number entering it. That is, the net magnetic flux out of any closed surface is zero. Gauss law signifies that magnetic mono poles does not exist.Every closed surface has magnetic flux in the inward direction to the south pole and equal flux in the outward direction to the north pole for a dipole. Since magnetic flux is not zero in the case of mono poles, it is a fact that mono poles do not exist.

E M B I B E

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise>Q 29

EASY

12th Karnataka Board

IMPORTANT

Earn 100

Write down Curie-Weiss law and write the value of curie temperature for iron.

Important Questions on Solved Physics Paper-2

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise>Q 30

What do you mean by electromagnetic induction? Write down Faraday's laws for electromagnetic induction and magnitude of induced emf?

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise-Choice>Q 31

Give the relation between V, N and I with respect to the primary and secondary coils of a transformer.

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise-Choice>Q 32

What is total internal reflection. Explain the phenomenon using Huygen's principle.

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise-Choice>Q 33

Find out the wavelength of the electron orbiting in the ground state of hydrogen atom.

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise-Choice>Q 35

A p-n photodiode is fabricated from a semiconductor with band gap of

2.8 eV

. Can it detect a wavelength of

6000 nm

?

h = 6 .626 \times 10^{- 34} Js

HARD

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise>Q 36

An electric dipole is formed by two charges $q$ and $- q$ placed at the two ends of an insulating rod of length $d$ and negligible mass. Write down the dipole moment. Is it a vector or a scalar? The dipole is then placed in a uniform electric field and is given a small angular displacement $θ$ from its equilibrium position. What are the total force and torque acting on it?

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise>Q 37

What is Wheatstone bridge, derive its balanced condition for balance using Kirchhoff's law.

MEDIUM

12th Karnataka Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 16 - Solved Physics Paper-2>Exercise-Choice>Q 38

A