Identify the INCORRECT statements from the following
Q. Identify the INCORRECT statements from the following :
A. Notation 2412Mg 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 $\lambda_1 = 900\ \text{nm}$ and energy $E_1$. Other radiation has wavelength $\lambda_2 = 300\ \text{nm}$ and energy $E_2$. $E_1 : E_2 = 3 : 1$.
D. Number of photons of light of wavelength $2000\ \text{pm}$ that provides $1\ \text{J}$ of energy is $1.006 \times 10^{16}$.
Correct Answer: A and C Only

Explanation

Let us check each statement one by one.

Statement A:
For 2412Mg:

Atomic number = 12 → Number of protons = 12
Number of neutrons = $24 - 12 = 12$

The statement says 24 protons and 12 neutrons, which is incorrect.
So, Statement A is incorrect.

Statement B:
Using relation:

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

$$ \lambda = \frac{3.0 \times 10^8}{4.5 \times 10^{15}} = 0.667 \times 10^{-7} = 6.67 \times 10^{-8}\ \text{m} $$

This matches the given value.
So, Statement B is correct.

Statement C:
Energy of radiation:

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

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

Thus,

$$ E_1 : E_2 = 1 : 3 $$

Given ratio is $3 : 1$, which is incorrect.
So, Statement C is incorrect.

Statement D:
Convert wavelength:

$$ 2000\ \text{pm} = 2 \times 10^{-9}\ \text{m} $$

Energy of one photon:

$$ E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{2 \times 10^{-9}} \approx 9.94 \times 10^{-17}\ \text{J} $$

Number of photons:

$$ n = \frac{1}{9.94 \times 10^{-17}} \approx 1.0 \times 10^{16} $$

Given value is correct.
So, Statement D is correct.

Therefore, the incorrect statements are A and C only.

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