The ${ }_{92}^{235} U$ atom disintegrates to ${ }_{82}^{207} Pb$ with a half-life of $10^9 \ yr$. In the process,it emits $7 \ \alpha$ particles and $n \ \beta^{-}$ particles. Here,$n$ is

Before the neutrino hypothesis,the beta decay process was thought to be the transition $n \to p + e^-$. If this were true,show that if the neutron was at rest,the proton and electron would emerge with fixed energies and calculate them. Experimentally,the electron energy was found to have a large range.

In a radioactive decay,an element $^A_Z X$ emits four $\alpha$-particles,three $\beta$-particles and eight $\gamma$-photons. The atomic number and mass number of the resulting final nucleus are

$A$ radio nuclide $A_1$ with decay constant $\lambda_1$ transforms into a radio nuclide $A_2$ with decay constant $\lambda_2$. If at the initial moment the preparation contained only the radio nuclide $A_1$,then the time interval after which the activity of the radio nuclide $A_2$ reaches its maximum value is:

The nucleus $_{90}Th^{228}$ transforms into $_{83}Bi^{212}$. How many $\alpha$-particles and $\beta$-particles are emitted during this process?

$A$ free neutron decays spontaneously into :