1

IIT-JEE 2004

Subjective
The Schrodinger wave equation for hydrogen atom is

$$\psi = {1 \over {4\sqrt {2\pi } }}{\left( {{1 \over {{a_0}}}} \right)^{3/2}}\left( {2 - {{{r_0}} \over {{a_0}}}} \right){e^{ - {r_0}/{a_0}}}$$
Where a0 is Bohr's radius. If the radial node in 2s be at r0, then find r0 in terms of a0.

2a0
2

IIT-JEE 2003

Subjective
Wavelength of high energy transition of H-atoms is 91.2 nm. Calculate the corresponding wavelength of He atoms.

22.8 nm
3

IIT-JEE 2000

Subjective
Calculate the energy required to excite one litre of hydrogen gas at 1 atm and 298 K to the first excited state of atomic hydrogen. The energy for the dissociation of H-H bond 436 kJ mol-1.

98.17 kJ
4

IIT-JEE 1996

Subjective
Consider the hydrogen atom to be a proton embedded in a cavity of radius a0 (Bohr radius) whose charge is neutralised by the addition of an electron to the cavity in vacuum, infinitely slowly. Estimate the average total energy of an electron in it's ground state in a hydrogen atom as the work done in the above neutralisation process. Also, if the magnitude of the average kinetic energy is half the magnitude of the average potential energy, find the average potential energy.

$- {{{e^2}} \over {4\pi \varepsilon {}_0.{a_0}}},{{ - {e^2}} \over {8\pi \varepsilon {}_0.{a_0}}}$