$A$ radioactive nucleus of mass number $A$,initially at rest,emits an $\alpha$-particle with a speed $v$. The recoil speed of the daughter nucleus will be

In the emission of $\gamma$-rays from a nucleus:

$A$ common example of alpha decay is ${ }_{92}^{238} U \longrightarrow{ }_{90}^{234} Th +{ }_{2}^{4} He + Q$. (Given: ${ }_{92}^{238} U = 238.05060 \, u$,${ }_{90}^{234} Th = 234.04360 \, u$,${ }_{2}^{4} He = 4.00260 \, u$,and $1 \, u = 931.5 \, MeV/c^2$). The energy released $(Q)$ during the alpha decay of ${ }_{92}^{238} U$ is $...... \, MeV$.

The intensity of gamma radiation from a given source is $I$. On passing through $36 \, mm$ of lead,it is reduced to $\frac{I}{8}$. The thickness of lead which will reduce the intensity to $\frac{I}{2}$ will be......$mm$

$A$ radioactive nucleus of mass $M$ emits a photon of frequency $v$ and the nucleus recoils. The recoil energy will be

If $_{92}U^{238}$ undergoes successively $8 \alpha$-decays and $6 \beta$-decays,then the resulting nucleus is