Identify the INCORRECT statements from the following: A. Notation \({}_{12}^{24} \mathrm{Mg}\) represents 24 protons and 12 neutrons. B. Wavelength of a radiation of frequency \(4.5 \times 10^{15} \mathrm{~s}^{-1}\) is \(6.7 \times 10^{-8} \mathrm{~m}\). C. One radiation has wavelength \(= \lambda_{1}(900 \mathrm{~nm})\) and energy \(=\mathrm{E}_{1}\). Other radiation has wavelength \(= \lambda_{2}(300 \mathrm{~nm})\) and energy \(=\mathrm{E}_{2}\). \(\mathrm{E}_{1}: \mathrm{E}_{2}=3: 1\). D. Number of photons of light of wavelength 2000 pm that provides 1 J of energy is \(1.006 \times 10^{16}\). Choose the correct answer from the options given below:

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Atomic Structure

Identify the INCORRECT statements from the following:
A. Notation

_{12}^{24} Mg

represents 24 protons and 12 neutrons.
B. Wavelength of a radiation of frequency

4.5 \times 1 0^{15} s^{- 1}

6.7 \times 1 0^{- 8} m

.
C. One radiation has wavelength

= λ_{1} (900 nm)

and energy

= E_{1}

. Other radiation has wavelength

= λ_{2} (300 nm)

and energy

= E_{2}

E_{1} : E_{2} = 3 : 1

.
D. Number of photons of light of wavelength 2000 pm that provides 1 J of energy is

1.006 \times 1 0^{16}

.

Choose the correct answer from the options given below:

Answer: (B)

The symbol

_{12}^{24} Mg

fixes the atomic number at

12

(twelve protons) and the mass number at

24

, leaving

24 - 12 = 12

neutrons, so the claim of twenty-four protons is wrong. The wavelength for

ν = 4.5 \times 1 0^{15} s^{- 1}

λ = c / ν = 6.7 \times 1 0^{- 8} m

, which is correct, and the photon count for

1

J at

2000

pm,

N = E λ / h c \approx 1.006 \times 1 0^{16}

, is also correct. Since energy varies inversely with wavelength,

E_{1} : E_{2} = λ_{2} : λ_{1} = 300 : 900 = 1 : 3

, not

3 : 1

, so that statement is wrong. The incorrect statements are the magnesium notation and the energy ratio.

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Single correct option