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Photons emitted by a gas consisting of excited hydrogen like atoms (A) during a transition from a higher quantum state (quantum no. n) to a lower quantum state (quantum no :m ) are incident on a metallic surface (B) causing the emission of photoelectrons . The fastest photoelectrons pass undeviated through a region consisting of electric field E_0 =3.7 V/cm and magnetic field B_0 =10^3T , oriented in perpecdicular directions and the photoelctrons enter the region perpendicular to both the electric and magnetic field The threshold wavelength for the metal B equal 830 nm. the spectrum of radiations emitted by the excited hydrogen -like atoms (A) consists of 15 different wavelengths . Find the quantum numbers of the states n,m and atomic number (Z) of the element (A) . (Take 1.89//13.6~~1//7)

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ANSWER :n=6, m=4 and z=2


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