Radioactive material 'A' has decay constant '8 $$\lambda $$' and material 'B' has decay constant '$$\lambda $$'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be e ?

If an electron in a hydrogen atom jumps from the 3^rd orbit to the 2^nd orbit, it emits a photon of wavelength $$\lambda $$. When it jumps from the 4^th orbit to the 3^rd orbit, the corresponding wavelength of the photon will be

The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is

When an $$\alpha $$-particle of mass m moving with velocity v bombards on a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as