A radio isotope $X$ with a half-life $1.4 \times 10^9$ years decays to $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$ in the ratio $1:7.$ The age of the rock is

If radius of the $^{27}_{13}Al$ nucleus is taken to be $R_{Al}$ then the radius of $^{125}_{53}Te$ nucleus is nearly

Radioactive material A has decay constant 8 $\lambda$ and material B has decay constant $\lambda.$ Initially, they have the same number of nuclei. After what time, the ratio of number of nuclei of material B to that of A will be $\frac{1}{e}$ ?

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

An $\alpha$-particle consists of:

The energy equivalent of $0.5$ g of a substance is:

The energy required to break one bond in DNA is $10^{-20}$ J$.$ This value in eV is nearly:

When a uranium isotope ${}^{235}_{92}U$ is bombarded with a neutron, it generates ${}^{89}_{36}Kr$, three neutrons and:

A radioactive nucleus $^{A}_{Z}X$ undergoes spontaneous decay in the sequence $^{A}_{Z}X \rightarrow _{Z-1}B \rightarrow _{Z-3}C \rightarrow _{Z-2}D$ where Z is the Z atomic number of element X. The possible decay particles in the sequence are:

The half-life of a radioactive nuclide is $100$ hours. The fraction of original activity that will remain after $150$ hours would be:

A nucleus with mass number 240 breaks into two fragments each of mass number 120. The binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the binding energy in the process is:

In the given nuclear reaction, the element X is:$\newline$ $^{22}_{11} Na \rightarrow X + e^{+} + {v}$

A nucleus of mass number $189$ splits into two nuclei having mass number $125$ and $64.$ The ratio of the radius of the two daughter nuclei is:

The half-life of a radioactive substance is 20 minutes. In how much time, the activity of the substance drops to $\frac{1}{16}$ of its initial value?

In the nuclear emission stated below, the mass number and atomic number of the product Q respectively, are:$\\ ^{200}_{82}X \xrightarrow{\alpha} Y \xrightarrow{e^+} Z \xrightarrow{\beta^-} P \xrightarrow{e^-} Q$