The activity of a radioactive material is 2.56 $$\times$$ 10^$$-$$3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 $$\times$$ 10^$$-$$5 Ci ?

Following statements related to radioactivity are given below :

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.

(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.

(C) Slope of the graph of log_e (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ($$\tau$$).

(D) Product of decay constant ($$\lambda$$) and half-life time (T_1/2) is not constant.

Choose the most appropriate answer from the options given below :

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, K_p are related as :

Given below are two statements :

Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E₁) to higher energy orbit (E₂), is given as hf = E₁ $$-$$ E₂

Statement II : The jumping of electron from higher energy orbit (E₂) to lower energy orbit (E₁) is associated with frequency of radiation given as f = (E₂ $$-$$ E₁)/h

This condition is Bohr's frequency condition.

In the light of the above statements, choose the correct answer from the options given below :