The total energy of an electron in the second excited state of hydrogen atom is about $$-1.51 \mathrm{~eV}$$. Its kinetic energy in this state is
After two hours one-eight of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is
In a radioactive material the activity at time t1, is A1 and at a later time t2, it is A2. If the decay constant of the material is $$\lambda$$, then
A proton has kinetic energy E = 100 eV which is equal to that of a photon. The wavelength of photon is $$\lambda$$2 and that of proton is $$\lambda$$1. The ratio $${{{\lambda _2}} \over {{\lambda _1}}}$$ is proportional to
The radius of a muonic hydrogen atom is 2.5 $$\times$$ 10$$-$$13 m. The total atomic volume (in m3) of a mole of such hydrogen atoms is (Take, $$\pi$$ = 3.14)
A radioactive sample at any instant has its disintegration rate 5000 disintegrations per min. After 5 min, the rate is 1250 disintegrations per min. Then, the disintegration constant (per min) is
Identify the hydrogen-like element whose spectral lines are four times shorter in wavelength compared to those of atomic hydrogen.
The decay constants of two radioactive substances X and Y are 4$$\lambda$$ and $$\lambda$$ respectively. At t = 0, a sample has the same number of two nuclei. The time taken for the ratio of number of nuclei to become $${1 \over {{e^3}}}$$ will be