JEE Chemistry 2026 Question with Solution

Given: Four statements about isotopic notation, wavelength-frequency relation, photon energy, and number of photons are to be checked.

Find: The incorrect statements and hence the correct option.

For A, in $^{24}_{12}Mg$, atomic number $Z = 12$ and mass number $A = 24$. Therefore,

$$\text{Number of protons} = Z = 12$$ $$\text{Number of neutrons} = A - Z = 24 - 12 = 12$$

The statement says $24$ protons and $12$ neutrons, so A is incorrect.

For B, wavelength is given by

$$\lambda = \frac{c}{\nu}$$

Substituting the values,

$$\lambda = \frac{3 \times 10^8}{4.5 \times 10^{15}} = 0.666 \times 10^{-7} \, \text{m} = 6.67 \times 10^{-8} \, \text{m}$$

This matches $6.7 \times 10^{-8} \, \text{m}$ approximately, so B is correct.

For C, photon energy is inversely proportional to wavelength:

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

Hence,

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

So the correct ratio is $1:3$, not $3:1$. Therefore, C is incorrect.

For D, if total energy is $E = 1 \, \text{J}$, then number of photons is

$$N = \frac{E\lambda}{hc}$$

Substituting,

$$N = \frac{1 \times 2000 \times 10^{-12}}{(6.626 \times 10^{-34})(3 \times 10^8)} \approx 1.006 \times 10^{16}$$

So D is correct.

Therefore, the incorrect statements are A and C, and the correct option is B.