Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

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.

Derive the equation of the balanced state in a Wheatstone bridge using Kirchhoff’s laws.

Read the following paragraph and answer the questions.

1. Why the image formed at infinity is often considered most suitable for viewing. Explain
2. In modern microscopes, multicomponent lenses are used for both the objective and the eyepiece. Why?
3. Write two points of difference between a compound microscope and an astronomical telescope
   OR
   Write two distinct advantages of a reflecting type telescope over a refracting type telescope.

With the help of a ray diagram explain the working of a reflecting telescope.

An alpha particle is accelerated through a potential difference of 100 V. Calculate:

1. The speed acquired by the alpha particle, and
2. The de-Broglie wavelength is associated with it.

(Take mass of alpha particle = 6.4 × 10⁻²⁷ kg)