A nucleus \({ }_{{n}}^{{m}} \mathrm{X}\) emits one $\mathrm{}$\(\alpha\text -\text{particle}\) and two \(\beta\text- \text{particle}\) The resulting nucleus is:

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:
1. Isobar of a parent.
2. Isomer of a parent.
3. Isotone of a parent.
4. Isotope of a parent.

The decay constants of two radioactive materials X₁ and X₂ are \(5\lambda\) and \(\lambda\) respectively. Initially, they have the same number of nuclei.  The ratio of the number of nuclei of X₁ to that of X₂  will be \(1/e\) after a time:
1. \(\lambda\)

2. \(\frac{1}{2\lambda }\)

3. \(\frac{1}{4\lambda }\)

4. \(\frac{e}{\lambda }\)

In the radioactive decay process, the negatively charged emitted β-particles are: