The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10^ -40 . An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.

Read the following statements and choose the correct option. (I) If the radius of the first Bohr orbit of hydrogen atom us redis of 2^(nd) orbit of Li^(2+) would be 4r (II) For s-orbital electron , the orbital angular momentum is zero

Obtain the first Bohr radius of muonic hydrogen atom [i.e., an atom in which a negatively charged muon (mu) of mass about 207m_e orbits around a proton].

The radius of the first electron orbit of a hydrogen atom is 0.5overset(@)A . The electron moves in this orbit with a uniform speed of 2.2xx10^(6)m.s^(-1). What is the magnetic field produced at the centre of the nucleus due to the motion of this electron?

Calculate the frequency of rtevolution of electron in the first Bohr orbit of hydrogen atom,if the radius of the first Bohr orbit is 0.5 overset @A and the velocity of electron in the first orbit is 2.24 xx 10^6 m s^(-1) .

In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 A. (a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at infinite separation of the electron from proton. (b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?

Agreat physicist of this century (RA.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~15 billion years) . From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants ?

In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 A: (a) Estimate the potential energy of the system in eV, if the zero of potential energy is taken at 1.06 overset @A separation of the electron from proton? (b) What is the minimum work required to free the electron, given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in (a)?

Calculate the magnitude of the electrostatic force exerted by the proton on the electron in the hydrogen atom and compare it with the weight of the electron. Given that mass of electron is 9.1 xx 10^-31 kg, charge on electron is 1.6 xx 10^-19 C and radius of hydrogen atom is 0.53 overset(@)A .