The mass of proton is 1.0073 u and that of neutron is $1.0087 \mathrm{u}(\mathrm{u}=$ atomic mass unit). The binding energy of ${ }_2 \mathrm{He}^4$ is

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