Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength \(\lambda\). The value of principal quantum number ' \(n\) ' of the excited state will be: (\(R\): Rydberg constant)

The resistance of a galvanometer is \(50\, ohm\) and the maximum current which can be passed through it is \(0.002\, A\). What resistance must be connected to it in order to convert it into an ammeter of range \(0 -0.5\, A\) ?....\(ohm\)

An electron, moving along the \(x-\) axis with an initial energy of \(100\, eV\), enters a region of magnetic field \(\vec B = (1.5\times10^{-3}T)\hat k\) at \(S\) (See figure). The field extends between \(x = 0\) and \(x = 2\, cm\). The electron is detected at the point \(Q\) on a screen placed \(8\, cm\) away from the point \(S\). The distance \(d\) between \(P\) and \(Q\) (on the screen) is :......\(cm\) (electron's charge \(= 1.6\times10^{-19}\, C\), mass of electron \(= 9.1\times10^{-31}\, kg\))

A \(5 \,V\) battery is connected across the points \(X\) and \(Y\). Assume \(D_{1}\) and \(D_{2}\) to be normal silicon diodes. Find the current (in \(A\)) supplied by the battery if the \(+ve\) terminal of the battery is connected to point \(X\)

A particle \(A\) of mass \(‘m’\) and charge \(‘q’\) is accelerated by a potential difference of \(50\, V\). Another particle \(B\) of mass \(‘4\, m’\) and charge \(‘q’\) is accelerated by a potential difference of \(2500\, V\). The ratio of de-Broglie wavelength \(\frac{{{\lambda _A}}}{{{\lambda _B}}}\) is close to

As per the given graph choose the correct representation for curve \(A\) and curve \(B\).Where \(X _{ C }=\) reactance of pure capacitive circuit connected with \(A.C.\) source \(X _{ L }=\) reactance of pure inductive circuit connected with \(A.C.\) source \(R =\) impedance of pure resistive circuit connected with \(A.C.\) source \(Z =\) Impedance of the LCR series circuit \(\}\)

A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is \(2 \mathrm{~cm} \times 2 \mathrm{~cm}\) and the area of the landscape photographed is \(400 \mathrm{~km}^2\). The focal length of the lens in the drone camera is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Statement I: Change in internal energy of a system containing \(n\) mole of ideal gas can be written as \(\Delta U = n C_v (T_f - T_i) = \dfrac{nR}{\gamma - 1}(T_f - T_i)\), where \(\gamma = \dfrac{C_p}{C_v}\), \(T_i =\) initial temperature, \(T_f =\) final temperature.
Statement II: Relation between degree of freedom \(f\) and \(\gamma (= C_p/C_v)\) is \(\left(\gamma = 1 + \dfrac{2}{f}\right)\)
Choose the correct answer from the options given below

For full scale deflection of total \(50\) divisions, \(50\,{mV}\) voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is \(2\, {div} / {mA}\) will be \(.....\Omega\)