Which of the following Statements is correct?

The question lists four statements related to nuclear physics. We check each one against standard theory and experimental facts.

Statement A: “The rate of radioactive decay cannot be controlled but that of nuclear fission can be controlled.”
• Spontaneous radioactive decay obeys $$N(t)=N_0 e^{-\lambda t}$$ where $$\lambda$$ (decay constant) is fixed by nuclear structure and is practically unaffected by temperature, pressure, electric or magnetic fields. • In a nuclear reactor the chain-reaction of fission is regulated by inserting or withdrawing control rods (Cd, B, Ag etc.) that absorb excess neutrons, and by moderators that slow down neutrons. Hence the fission rate is indeed controllable.
Therefore Statement A is correct.

Statement B: “Nuclear forces are short range, attractive and charge dependent.”
• They are certainly short-range (effective up to ≈1-2 fm) and attractive. • However, nuclear forces are charge independent: the n-n, p-p and n-p interactions are almost identical after electromagnetic effects are removed. Hence the phrase “charge dependent” is wrong ⇒ Statement B is incorrect.

Statement C: “Nuclei of atoms having same number of neutrons are known as isobars.”
• Same neutron number (N) → isotones. • Same mass number (A) → isobars. Thus Statement C interchanges the definitions and is incorrect.

Statement D: “Wavelength of matter waves is given by de Broglie formula but that of photons is not given by the same formula.”
• de Broglie relation: $$\lambda=\frac{h}{p}$$ holds for any particle with momentum $$p$$. • For a photon, $$p=\frac{h}{\lambda}$$, leading to the identical relation $$\lambda=\frac{h}{p}$$. Hence the formula applies to photons as well, making Statement D incorrect.

Only Statement A stands true. Therefore,

Option A which is: The rate of radioactive decay cannot be controlled but that of nuclear fission can be controlled.