An electron, a doubly ionized helium ion (He++) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths $$\lambda$$e, $$\lambda$$He++ and $$\lambda$$p is :

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4.64 $$\times$$ 10–26 kg, Boltzman constant: 1.38 $$\times$$ 10–23 J/K, Planck constant : 6.63 $$\times$$ 10–34 J.s)

Particle A of mass mA = {m \over 2} moving along the x-axis with velocity v0 collides elastically with another particle B at rest having mass mB = {m \over 3}. If both particles move along the x-axis after the collision, the change $$\Delta$$$$\lambda$$ in de-Broglie wavlength of particle A, in terms of its de-Broglie wavelength ($$\lambda$$0) before collision is :

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 $$\times$$ 10–4. The mass of the particle is close to

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)

When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy TA eV end de-Broglie wavelength $${\lambda }_A$$. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is TB = (TA – 1.5) eV. If the de-Broglie wavelength of these photoelectrons $${\lambda }_B$$ = 2$${\lambda }_A$$, then the work function of metal B is :

An electron (mass m) with initial velocity $$\overrightarrow{v}=v_0\hat{i}+v_0\hat{j}$$ is in an electric field $$\overrightarrow{E}=-E_0\hat{k}$$. If $${\lambda }_0$$ is initial de-Broglie wavelength of electron, its de-Broglie wave length at time t is given by :

A particle moving with kinetic energy E has de Broglie wavelength $$\lambda$$. If energy $$\Delta$$E is added to its energy, the wavelength become $$\lambda$$/2. Value of $$\Delta$$E, is :

Radiation, with wavelength 6561 $$\stackrel{o}{A}$$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10–4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :

An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is :

The figure gives experimentally measured B vs H variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are :

A small bar magnet placed with its axis at 30o with an external field of 0.06 T experiences a torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is :

Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $$\overrightarrow{B}$$ . Then the field inside the paramagnetic substance is :

A paramagnetic sample shows a net magnetisation of 6 A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be:

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius Re . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become \sqrt {{3 \over 2}} times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :

The mass density of a planet of radius R varies with the distance r from its centre as $$\rho$$(r) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right). Then the gravitational field is maximum at :

On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is given by {{Ax} \over {{{\left( {{x^2} + {a^2}} \right)}^{3/2}}}} in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is:

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

The value of the acceleration due to gravity is g1 at a height h = {R \over 2} (R = radius of the earth) from the surface of the earth. It is again equal to g1 at a depth d below the surface of the earth. The ratio \left( {{d \over R}} \right) equals :