An $$\alpha $$-particle of energy $$5$$ $$MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is of the order of

In the nuclear fusion reaction $$${}_1^2H + {}_1^3H \to {}_2^4He + n$$$
given that the repulsive potential energy between the two nuclei is $$ \sim 7.7 \times {10^{ - 14}}J$$, the temperature at which the gases must be heated to initiate the reaction is nearly
[ Boltzmann's Constant $$k = 1.38 \times {10^{ - 23}}\,J/K$$ ]

Which of the following cannot be emitted by radioactive substances during their decay ?

A radioactive sample at any instant has its disintegration rate $$5000$$ disintegrations per minute. After $$5$$ minutes, the rate is $$1250$$ disintegrations per minute. Then, the decay constant (per minute) is