Structure of Atom

Let, number of photons $=n$

$\therefore \quad E=n \cdot h v=n \cdot \frac{h c}{\lambda}$

where, $v=$ frequency, $c=$ velocity of light, $\lambda=$ wavelength

$\therefore \quad n=\frac{E \times \lambda}{h c}=\frac{3 \times 10^{-18} \mathrm{~J} \times 660 \times 10^{-9} \mathrm{~m}}{6.6 \times 10^{-34} \mathrm{Js} \times 3 \times 10^8 \mathrm{~ms}^{-1}}=10$

$n=10$

So, the number of emitted photon $=10$

Hence, option (b) is the correct.

Assertion : The chemical properties of different isotopes are the same.

Reason : Isotopes have the same number of neutrons.

Option C

If assertion is true, but reason is false.

The chemical properties of different isotopes are indeed the same because chemical properties are determined by the number of electrons and the arrangement of electrons in an atom, which is defined by the atomic number (number of protons). Isotopes of an element have the same atomic number but different numbers of neutrons. Therefore, they exhibit the same chemical behavior.

However, the reason given is incorrect because isotopes of an element do not have the same number of neutrons. Instead, isotopes are variants of a particular chemical element that have the same number of protons but a different number of neutrons.

$\begin{aligned} & \text { Given, } E_0=4.2 \mathrm{~eV} \\ & =4.2 \times 1.60 \times 10^{-19} \mathrm{~J} \\ & =6.72 \times 10^{-19} \mathrm{~J} \\ & \because \quad E=h \nu=\frac{h c}{\lambda} \\ & \therefore \quad E=\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{2000 \times 10^{-10}} \\ & =9.94 \times 10^{-19} \mathrm{~J} \\ \end{aligned}$

$\therefore$ Kinetic energy of electron emitted

$\begin{aligned} & =(9.94-6.72) \times 10^{-19} \mathrm{~J} \\ & =3.22 \times 10^{-19} \mathrm{~J} \end{aligned}$