Structure of Atom Part 3

Concept:Understanding nuclear notation, wave properties of light ($\lambda = c/\nu$), energy-wavelength relation ($E \propto 1/\lambda$), and photon energy calculation.Explanation:Statement A: For ${}_{12}^{24}\mathrm{Mg}$, atomic number $Z=12$ gives 12 protons, mass number $A=24$ gives 12 neutrons. The statement claims 24 protons and 12 neutrons, which is wrong. So A is incorrect.Statement B: Using $\lambda = c/\nu$, with $c=3\times10^8\ \mathrm{m\ s^{-1}}$ and $\nu=4.5\times10^{15}\ \mathrm{s^{-1}}$, we get $\lambda = (3\times10^8)/(4.5\times10^{15}) = 6.67\times10^{-8}\ \mathrm{m}$. This matches the given $6.7\times10^{-8}\ \mathrm{m}$. So B is correct.Statement C: Energy $E = hc/\lambda$, so $E \propto 1/\lambda$. Thus $E_1/E_2 = \lambda_2/\lambda_1 = 300/900 = 1/3$, giving $E_1:E_2 = 1:3$. The statement says $3:1$, which is incorrect. So C is incorrect.Statement D: Wavelength $\lambda = 2000\ \mathrm{pm} = 2\times10^{-9}\ \mathrm{m}$. Energy per photon $E = (6.626\times10^{-34}\times3\times10^8)/(2\times10^{-9}) = 9.939\times10^{-17}\ \mathrm{J}$. Number of photons for 1 J: $N = 1/9.939\times10^{-17} = 1.006\times10^{16}$. This matches the given value. So D is correct.Answer:The incorrect statements are A and C only. Therefore the correct option is B.