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

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.

Fusion processes, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact ______.

1. nuclear forces have short range.
2. nuclei are positively charged.
3. the original nuclei must be completely ionized before fusion can take place.
4. the original nuclei must first break up before combining with each other.

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)

An electron is accelerated from rest through a potential difference of 100 V. Find:

1. the wavelength associated with
2. the momentum and
3. the velocity required by the electron.

A cell of emf E is connected across an external resistance R. When current 'I' is drawn from the cell, the potential difference across the electrodes of the cell drops to V. The internal resistance 'r' of the cell is ______.

In the given figure the radius of curvature of the curved face in the planoconvex and the planoconcave lens is 15 cm each. The refractive index of the material of the lenses is 1.5. Find the final position of the image formed.

Which of the following graphs correctly represents the variation of a particle momentum with its associated de-Broglie wavelength?

How will the de-Broglie wavelength associated with an electron be affected when the velocity of the electron decreases? Justify your answer.

How will the de-Broglie wavelength associated with an electron be affected when the accelerating potential is increased? Justify your answer.

Three cells, each of emf E but internal resistances 2r, 3r and 6r are connected in parallel across a resistor R.

Obtain expressions for (i) current flowing in the circuit, and (ii) the terminal potential differences across the equivalent cell.