The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr’s quantization rule for angular momentum is valid in the case of gravitation.

(a) Calculate the minimum radius the earth can have for its orbit.

(b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 10²⁴ kg, mass of the sun = 2.0 × 10³⁰ kg, earth-sun distance =1.5 × 10¹¹ m.

Radiation from hydrogen discharge tube falls on a cesium plate. Find the maximum possible kinetic energy of the photoelectrons. Work function of cession is 1.9 eV.

A filter transmits only the radiation of wavelength greater than 440 nm. Radiation from a hydrogen discharge tube goes through such a filter and is incident on a metal of work function 2.0 eV. Find the stopping potential which can stop the photoelectrons.

Consider a neutron and an electron bound to each other due to gravitational force. Assuming Bohr’s quantization rule for angular momentum to be valid in this case, derive an expression for the energy of the neutron-electron system.

A uniform magnetic field B exists in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr’s quantization rule for angular momentum, calculate

(a) the smallest possible radius of the electron

(b) the radius of the nth orbit and

(c) the minimum possible speed of the electron.