modern physics revision

its like i gave for optics

1]if an x ray tube operates at voltage of 10000 volts, find the ratio of the de broglie wavelength of the incident electrons to the shortest wavelength of X rays produced. the specific charge of electron is 1.8 x10¹¹ C/kg

2] the wavelength of first line of lyman series for hydrogen is identical to that of second line f balmer series for some hydrpgen like ion `x`. calculate energies of first four levels of `x`.

3]an imaginary particle has a charge equal to that of an electron and mass 100 times the mass of electron of the electron. it moves in a circular orbit around a nucleus of charge +4e. take the mass of the nucleus to be ∞. assuming that the bohr`s model is applicable to this system.
a] Derive an expression for the radius of nth bohr orbit.
b]find the wavelength of the radiation emitted when the particle jumps from fourth orbit to the second orbit.

4]A 100 W bulb is placed at the centre of a spherical chamber of radius 20 cm. assume that 60% of the energy supplied to the bulb is converted into light and that the surface of the chamber is a perfect absorber. find the pressure exerted by light on the surface of the chamber.