Imagine that the electron in a hydrogen atom is replaced by a muon \((\mu) .\) The mass of muon particle is \(207\) times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be ............. \(eV\)

The energy of \(He ^{+}\)ion in its first excited state is \(......eV\) (The ground state energy for the Hydrogen atom is \(-13.6\,eV )\)

Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) is

Light is incident on a metallic plate having work function \( 110\times10^{-20} \) J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is __________ rad/s. (\( h=6.63\times10^{-34} \) J.s)

A spherical soap bubble of radius \(3\,cm\) is formed inside another spherical soap bubble of radius \(6\,cm\). If the internal pressure of the smaller bubble of radius \(3\,cm\) in the above system is equal to the internal pressure of the another single soap bubble of radius \(r\,cm\). The value of \(r\) is.......

A gas molecule of mass \(M\) at the surface of the Earth has kinetic energy equivalent to \(0\,^oC\). If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (\(k_B\) is Boltzmann constant)

In a potentiometer arrangement, a cell gives a balancing point at \(75\, cm\) length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is \(3: 2\), the difference in the balancing length of the potentiometer wire in above two cases will be.........\(cm .\)

The terminal velocity \(\left( v _{ t }\right)\) of the spherical rain drop depends on the radius ( \(r\) ) of the spherical rain drop as

In two separate Young's double-slit experimental set-ups, two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slit separations and that of the wavelengths of light used are \(2: 1\) and \(1: 2\) respectively. The corresponding ratio of the distances between the slits and the respective screens ( \(D_1 / D_2\) ) is ___________ .

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :