$A$ bulb is rated at $150 \text{ W}$,converting $8\%$ of its energy into light. If the energy of one photon is $4.42 \times 10^{-19} \text{ J}$,how many photons are emitted by the bulb per second?

Which one of the following about an electron occupying the $1s$ orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by $a_0$)

Answer the following by appropriately matching the lists based on the information given in the paragraph. Consider Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following,$List-I$ contains some quantities for the $n^{\text{th}}$ orbit of the atom and $List-II$ contains options showing how they depend on $n$.

$List-I$	$List-II$
$(I)$ Radius of the $n^{\text{th}}$ orbit	$(P) \propto n^{-2}$
$(II)$ Angular momentum of the electron in the $n^{\text{th}}$ orbit	$(Q) \propto n^{-1}$
$(III)$ Kinetic energy of the electron in the $n^{\text{th}}$ orbit	$(R) \propto n^0$
$(IV)$ Potential energy of the electron in the $n^{\text{th}}$ orbit	$(S) \propto n^1$
-	$(T) \propto n^2$
-	$(U) \propto n^{1/2}$

$(1)$ Which of the following options has the correct combination considering $List-I$ and $List-II$?
$(1) (II), (R)$ $(2) (I), (P)$ $(3) (I), (T)$ $(4) (II), (Q)$
$(2)$ Which of the following options has the correct combination considering $List-I$ and $List-II$?
$(1) (III), (S)$ $(2) (IV), (Q)$ $(3) (IV), (U)$ $(4) (III), (P)$
Give the answer for questions $(1)$ and $(2)$.

The wavelength of a spectral line for an electronic transition is inversely related to :

$A$ $100 \ W$ bulb emits light of wavelength '$x$' $\mathring{A}$. What is the value of $x$,if the number of photons emitted is $2.0 \times 10^{20} \ s^{-1}$? $(h = 6.63 \times 10^{-34} \ J \cdot s, c = 3 \times 10^8 \ m \cdot s^{-1})$

$A$ bulb emits light of wavelength $4500 \ \mathring{A}$. The bulb is rated at $150 \ \text{W}$ and $8\%$ of the energy is emitted as light. How many photons are emitted by the bulb per second?