Question

Identify the INCORRECT statements from the following:

A. Notation \( {}^{24}_{12}\mathrm{Mg} \) represents 24 protons and 12 neutrons.
B. Wavelength of a radiation of frequency \( 4.5 \times 10^{15}\ \text{s}^{-1} \) is \( 6.7 \times 10^{-8}\ \text{m} \).
C. One radiation has wavelength \( \lambda_1 \) (900 nm) and energy \( E_1 \). Other radiation has wavelength \( \lambda_2 \) (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 \( 1.006 \times 10^{16} \).

Choose the correct answer from the options given below: 

• A. A and D Only
• B. A and C Only
• C. A and B Only
• D. B and C Only

Hint:

Remember the relationships between Z, A, protons, and neutrons. Energy and wavelength are inversely related for photons.

Answer 1

The Correct Option is B

A. The nucleus $^{24}_{12}Mg$ has $Z=12$ protons and $A-Z = 24-12 = 12$ neutrons.
The statement says 24 protons and 12 neutrons. Incorrect.
B. $\lambda = c/\nu = \frac{3 \times 10^8}{4.5 \times 10^{15}} = 0.666 \times 10^{-7} \text{ m} = 6.67 \times 10^{-8} \text{ m}$.
The statement says $6.7 \times 10^{-8} \text{ m}$. Correct.
C. Energy $E \propto 1/\lambda$. $\frac{E_1}{E_2} = \frac{\lambda_2}{\lambda_1} = \frac{300 \text{ nm}}{900 \text{ nm}} = \frac{1}{3}$.
The statement says $3:1$. Incorrect.
D. $N = \frac{E \lambda}{hc} = \frac{1 \times 2000 \times 10^{-12}}{(6.626 \times 10^{-34})(3 \times 10^8)} \approx 1.006 \times 10^{16}$. Correct.
The INCORRECT statements are A and C.