For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

The box of a pin hole camera, of length \(L\), has a hole of radius \(a\). It is assumed that when the hole is illuminated by a parallel beam of light of wavelength \(\lambda\), the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size ( say \(b_{min}\)) when

In series \(LCR\) circuit, the capacitance is changed from \(\mathrm{C}\) to \(4 \mathrm{C}\). To keep the resonance frequency unchanged, the new inductance should be _______.

A simple pendulum of length \(L\) is placed between the plates of a parallel plate capacitor having electric field \(E,\) as shown in figure. Its bob has mass \(m\) and charge \(q.\) the time period of the pendulum is given by

Two parallel plate capacitors of capacity \(C\) and \(3\,C\) are connected in parallel combination and charged to a potential difference \(18\,V\). The battery is then disconnected and the space between the plates of the capacitor of capacity \(C\) is completely filled with a material of dielectric constant \(9\). The final potential difference across the combination of capacitors will be \(V\)

Consider the following radioactive decay process  \({ }_{84}^{218} A \stackrel{\alpha}{\longrightarrow} A_1 \stackrel{\beta^{-}}{\longrightarrow} A_2 \stackrel{\gamma}{\longrightarrow} A_3 \stackrel{\alpha}{\longrightarrow} A_4 \stackrel{B^{+}}{\longrightarrow} A_5 \stackrel{\gamma}{\longrightarrow} A_6\) The mass number and the atomic number \(A _6\) are given by 

A body is projected from the ground at an angle of \(45^{\circ}\) with the horizontal. Its velocity after \(2s\) is \(20 \,ms ^{-1}\). The maximum height reached by the body during its motion is \(m\). (use \(g =10\, ms ^{-2}\) )

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is \(11.2 \mathrm{~km} / \mathrm{s}\), the escape velocity in \(\mathrm{km} / \mathrm{s}\) from the planet will be :

Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vernier scale is _______.

The volume of an ideal gas increases 8 times and temperature becomes (1/4) of initial temperature during a reversible change. If there is no exchange of heat in this process (\( \Delta Q=0 \)) then identify the gas from the following options:

How many alpha and beta particles are emitted when Uranium \({ }_{92} U ^{238}\) decays to lead \({ }_{82} Pb ^{206}\) ?

A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now ..... \(f\)