In the following nuclear reaction,
$D\stackrel{\alpha }{\to }{D}_1\stackrel{{\beta }^{-}}{\to }{D}_2\stackrel{\alpha }{\to }{D}_3\stackrel{\gamma }{\to }{D}_4$
Mass number of $D$ is $182$ and atomic number is $74$ . Mass number and atomic number of $D_4$ respectively will be

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$. The value of principal quantum number $n$ of the excited state will be :

( $R:$ Rydberg constant)

$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) third permitted energy level to the second level and

(ii) the highest permitted energy level to the second permitted level.

The value of $x$ will be

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute. $10$ minutes later, the rate becomes $2250$ disintegrations per minute. The approximate decay constant is

(Take ${\log }_{10}1.88=0.63$)

Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:

 ${}_1{}^{2}X+{}_1{}^{2}X={}_2{}^{4}Y$

 The binding energies per nucleon ${}_1{}^{2}X$ and ${}_2{}^{4}Y$ are $1.1\mathrm{MeV}$ and $7.6\mathrm{MeV}$ respectively. The energy released in this process is_____ $\mathrm{MeV}$.