Science (English Medium) Class 12 - CBSE Question Bank Solutions

Consider a light beam incident from air to a glass slab at Brewster’s angle as shown in figure. A polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid.

Can reflection result in plane polarised light if the light is incident on the interface from the side with higher refractive index?

For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of 5000 Å and electrons accelerated through 100 V used as the illuminating substance.

Figure shown a two slit arrangement with a source which emits unpolarised light. P is a polariser with axis whose direction is not given. If I₀ is the intensity of the principal maxima when no polariser is present, calculate in the present case, the intensity of the principal maxima as well as of the first minima.

To ensure almost 100 per cent transmissivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF₂ (n = 1.38). What should the thickness of the film be so that at the center of the visible spectrum (5500 Å) there is maximum transmission.

A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to ______.

A proton, a neutron, an electron and an α-particle have same energy. Then their de Broglie wavelengths compare as ______.

An electron is moving with an initial velocity `v = v_0hati` and is in a magnetic field `B = B_0hatj`. Then it’s de Broglie wavelength ______.

An electron (mass m) with an initial velocity `v = v_0hati (v_0 > 0)` is in an electric field `E = - E_0hati `(E₀ = constant > 0). It’s de Broglie wavelength at time t is given by ______.

An electron (mass m) with an initial velocity `v = v_0hati` is in an electric field `E = E_0hatj`. If λ₀ = h/mv₀, it’s de Broglie wavelength at time t is given by ______.

Relativistic corrections become necessary when the expression for the kinetic energy `1/2 mv^2`, becomes comparable with mc², where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?

1. λ = 10 nm
2. λ = 10^–1 nm
3. λ = 10^–4 nm
4. λ = 10^–6 nm

Two particles A₁ sand A₂ of masses m₁, m₂ (m₁ > m₂) have the same de Broglie wavelength. Then ______.

1. their momenta are the same.
2. their energies are the same.
3. energy of A₁ is less than the energy of A₂.
4. energy of A₁ is more than the energy of A₂.

The de Broglie wavelength of a photon is twice the de Broglie wavelength of an electron. The speed of the electron is `v_e = c/100`. Then ______.

1. `E_e/E_p = 10^-4`
2. `E_e/E_p = 10^-2`
3. `p_e/(m_ec) = 10^-2`
4. `p_e/(m_ec) = 10^-4`

A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values λ₁, λ₂ with λ₁ > λ₂. Which of the following statement are true?

1. The particle could be moving in a circular orbit with origin as centre.
2. The particle could be moving in an elliptic orbit with origin as its focus.
3. When the de Broglie wavelength is λ₁, the particle is nearer the origin than when its value is λ₂.
4. When the de Broglie wavelength is λ₂, the particle is nearer the origin than when its value is λ₁.

A proton and an α-particle are accelerated, using the same potential difference. How are the de-Broglie wavelengths λp and λ_a related to each other?

Assuming an electron is confined to a 1 nm wide region, find the uncertainty in momentum using Heisenberg Uncertainty principle (∆x∆p ≃ h). You can assume the uncertainty in position ∆x as 1 nm. Assuming p ≃ ∆p, find the energy of the electron in electron volts.

Two particles A and B of de Broglie wavelengths λ₁ and λ₂ combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).

A particle A with a mass m _A is moving with a velocity v and hits a particle B (mass m_B) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.

For the transistor circuit shown in figure, evaluate V_E, R_B, R_E given I_C = 1 mA, V_CE = 3 V, V_BE = 0.5 V and V_CC = 12 V, β = 100.

State the two Kirchhoff’s rules used in the analysis of electric circuits and explain them.