JEE Main 2026 — 23 January, Evening Shift — Question 57

A: $^{24}_{12}\mathrm{Mg}$ has 12 protons and 12 neutrons. Statement A is incorrect.

B: $\lambda = \frac{c}{\nu} = \frac{3 \times 10^8}{4.5 \times 10^{15}} = 6.7 \times 10^{-8}\,\mathrm{m}$

Statement B is correct.

C: $E \propto \frac{1}{\lambda}$

$\frac{E_1}{E_2} = \frac{\lambda_2}{\lambda_1} = \frac{300}{900} = \frac{1}{3}$

So $E_1 : E_2 = 1 : 3$

Statement C is incorrect.

D: Energy of one photon, $E = \frac{hc}{\lambda} = \frac{6.6 \times 10^{-34} \times 3 \times 10^8} {2 \times 10^{-9}} = 9.9 \times 10^{-17}\,\mathrm{J}$

Number of photons, $n = \frac{1}{9.9 \times 10^{-17}} = 1.01 \times 10^{16}$

Statement D is correct. Thus, incorrect statements are A and C.