The de-Broglie wavelength ($$\lambda $$_B) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state ($$\lambda $$_G) by :

Both the nucleus and the atom of some element arein their respective first excited states. They get de-excted by emitting photons of wavelengths ^{$$\lambda $$}N, ^{$$\lambda $$}A respectively. The ratio $${{{}^\lambda N} \over {{}^\lambda A}}$$is closest to :

At some instant, a radioactive sample S₁ having an activity 5 $$\mu $$Ci has twice the number of nuclei as another sample S₂ which has an activity of 10 $$\mu $$Ci. The half lives of S₁ and S₂ are :

The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :