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

Calculate the de Broglie wavelength of the electrons accelerated through a potential difference of 56 V.

What is the

(a) momentum,

(b) speed, and

(c) de Broglie wavelength of an electron with kinetic energy of 120 eV.

The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which

(a) an electron, and

(b) a neutron, would have the same de Broglie wavelength.

What is the de Broglie wavelength of a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s?

What is the de Broglie wavelength of a ball of mass 0.060 kg moving at a speed of 1.0 m/s?

What is the de Broglie wavelength of a dust particle of mass 1.0 × 10⁻⁹ kg drifting with a speed of 2.2 m/s?

An electron and a photon each have a wavelength of 1.00 nm. Find

(a) their momenta,

(b) the energy of the photon, and

(c) the kinetic energy of electron.

For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 × 10⁻¹⁰ m?

Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).

What is the de Broglie wavelength of a nitrogen molecule in air at 300 K? Assume that the molecule is moving with the root-mean square speed of molecules at this temperature. (Atomic mass of nitrogen = 14.0076 u)

Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wavelength of the probe equal to 1 Å, which is of the order of inter-atomic spacing in the lattice) (m_e = 9.11 × 10⁻³¹ kg).

Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. (m_n= 1.675 × 10⁻²⁷ kg)

Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27°C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27°C) and 1 atm pressure, and compare it with the mean separation between two atoms under these conditions.

Compute the typical de Broglie wavelength of an electron in a metal at 27°C and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10⁻¹⁰ m.

The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:

E = hv, p = `"h"/lambda`

But while the value of λ is physically significant, the value of v (and therefore, the value of the phase speed vλ) has no physical significance. Why?

Unpolarised light is passed through a polaroid P₁. When this polarised beam passes through another polaroid P₂ and if the pass axis of P₂ makes angle θ with the pass axis of P₁, then write the expression for the polarised beam passing through P₂. Draw a plot showing the variation of intensity when θ varies from 0 to 2π.

The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for

1. the current draw from the cell and
2. the power consumed in the network.

Why should the objective of a telescope have large focal length and large aperture? Justify your answer.