1
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1
Out of Syllabus

Assume that protons and neutrons have equal masses. Mass of a nucleon is $$1.6\times10^{-27}$$ kg and radius of nucleus is $$1.5\times10^{-15}~\mathrm{A^{1/3}}$$ m. The approximate ratio of the nuclear density and water density is $$n\times10^{13}$$. The value of $$n$$ is __________.

2
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Out of Syllabus

Two radioactive materials A and B have decay constants $$25 \lambda$$ and $$16 \lambda$$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $$\frac{1}{a \lambda}$$. The value of a is _________.

3
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1
Out of Syllabus

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be _________ hours.

4
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

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 for $$\frac{2}{1} X$$ and $${ }_{2}^{4} Y$$ are $$1.1 \,\mathrm{MeV}$$ and $$7.6 \,\mathrm{MeV}$$ respectively. The energy released in this process is _______________ $$\mathrm{MeV}$$.